HP 50g user´s manual

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HP 50g graphing calculator
user’s manual
H
Edition 1
HP part number F22
29AA-90001
Notice
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THIS MANUAL AND ANY EXAMPLES CONTAINED HEREIN ARE 
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NOTICE. HEWLETT-PACKARD COMPANY MAKES NO 
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OF MERCHANTAB
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USE OF THIS M
HEREIN.
© Copyright 2003, 2
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Edition 1 
FrontPageQS49_E.backup.fm Page 2 Friday, February 24, 2006 4:54 PM
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ILITY, NON-INFRINGEMENT AND FITNESS 
R PURPOSE.
D CO. SHALL NOT BE LIABLE FOR ANY 
NCIDENTAL OR CONSEQUENTIAL DAMAGES 
WITH THE FURNISHING, PERFORMANCE, OR 
ANUAL OR THE EXAMPLES CONTAINED 
006 Hewlett-Packard Development Company, L.P.
ation, or translation of this manual is prohibited 
permission of Hewlett-Packard Company, except as 
pyright laws. 
pany 
n Rd, 
April 2006
Preface
You have in your hands a compact symbolic and numerical computer that 
will facilitate calculation and mathematical analysis of problems in a 
variety of disciplines, from elementary mathematics to advanced 
engineering and science subjects. 
This manual contains examples that illustrate the use of the basic calculator 
functions and operations. The chapters in this user’s manual are organized 
by subject in order of difficulty: from the setting of calculator modes, to real 
and complex number calculations, operations with lists, vectors, and 
matrices, graphics, calculus applications, vector analysis, differential 
equations, probability and statistics.
For symbolic operations the calculator includes a powerful Computer 
Algebraic System (CAS), which lets you select different modes of operation, 
e.g., complex numbers vs. real numbers, or exact (symbolic) vs. 
approximate (numerical) mode. The display can be adjusted to provide 
textbook-type expressions, which can be useful when working with 
matrices, vectors, fractions, summations, derivatives, and integrals. The 
high-speed graphics of the calculator are very convenient for producing 
complex figures in very little time.
Thanks to the infrared port, the USB port, and the RS232 port and cable 
provided with your calculator, you can connect your calculator with other 
calculators or computers. This allows for fast and efficient exchange of 
programs and data with other calculators and computers.
We hope your calculator will become a faithful companion for your school 
and professional applications.
SG49A.book Page 1 Friday, September 16, 2005 1:31 PM
Page TOC-1
Table of Contents
Chapter 1 - Getting started
Basic Operations, 1-1
Batteries, 1-1
Turning the ca
Adjusting the 
Contents of th
Menus, 1-3
The TOOL me
Setting time a
Introducing the ca
Selecting calculato
Operating Mo
Number Form
Standard fo
Fixed forma
Scientific fo
Engineering
Decimal co
Angle Measur
Coordinate Sy
Selecting CAS sett
Explanation o
Selecting Display 
Selecting the d
Selecting prop
Selecting prop
Selecting prop
References, 1-20
Chapter 2 - Intr
Calculator objects
SG49A.book Page 1 Friday, September 16, 2005 1:31 PM
lculator on and off, 1-2
display contrast, 1-2
e calculator’s display, 1-3
nu, 1-3
nd date, 1-4
lculator’s keyboard, 1-4
r modes, 1-6
de, 1-7
at and decimal dot or comma, 1-10
rmat, 1-10
t with decimals, 1-10
rmat, 1-11
 format, 1-12
mma vs. decimal point, 1-13
e, 1-14
stem, 1-14
ings, 1-15
f CAS settings, 1-16
modes, 1-17
isplay font, 1-18
erties of the line editor, 1-18
erties of the Stack, 1-19
erties of the equation writer (EQW), 1-20
oducing the calculator
, 2-1
Editing expressions in the stack, 2-1
Creating arithmetic expressions, 2-1
Creating algebraic expressions, 2-4
Using the Equation Writer (EQW) to create expressions, 2-5
Creating arithmetic expressions, 2-5
Creating algebraic expressions, 2-7
Organizing data i
The HOME di
Subdirectories
Variables, 2-9
Typing variab
Creating varia
Algebraic m
RPN mode,
Checking vari
Algebraic m
RPN mode,
Using the ri
Listing the c
Deleting varia
Using funct
Using funct
UNDO and CMD f
CHOOSE boxes vs
References, 2-18
Chapter 3 - Cal
Examples of real n
Using powers
Real number funct
Using calculat
Hyperbolic fun
Operations with u
The UNITS me
SG49A.book Page 2 Friday, September 16, 2005 1:31 PM
Page TOC-2
n the calculator, 2-8
rectory, 2-8
, 2-9
le names , 2-9
bles, 2-10
ode, 2-10
 2-11
ables contents, 2-13
ode, 2-13
 2-13
ght-shift key followed by soft menu key labels, 2-13
ontents of all variables in the screen, 2-14
bles, 2-14
ion PURGE in the stack in Algebraic mode, 2-14
ion PURGE in the stack in RPN mode, 2-15
unctions, 2-16
. Soft MENU, 2-16
culations with real numbers
umber calculations, 3-1
 of 10 in entering data, 3-3
ions in the MTH menu, 3-5
or menus, 3-5
ctions and their inverses, 3-5
nits, 3-7
nu, 3-7
Page TOC-3
Available units, 3-9
Attaching units to numbers, 3-9
Unit prefixes, 3-10
Operations with units, 3-11
Unit conversions, 3-12
Physical constants in the calculator, 3-13
Defining and usin
Reference, 3-16
Chapter 4 - Cal
Definitions, 4-1
Setting the calcula
Entering comp
Polar represen
Simple operations
The CMPLX menus
CMPLX menu 
CMPLX menu 
Functions applied 
Function DROITE: 
Reference, 4-7
Chapter 5 - Alg
Entering algebraic
Simple operations
Functions in th
Operations with tr
Expansion an
Expansion an
Functions in the A
Polynomials, 5-8
The HORNER
The variable V
The PCOEF fu
SG49A.book Page 3 Friday, September 16, 2005 1:31 PM
g functions, 3-15
culations with complex numbers
tor to COMPLEX mode, 4-1
lex numbers, 4-2
tation of a complex number, 4-3
 with complex numbers, 4-4
, 4-4
through the MTH menu, 4-4
in keyboard, 4-6
to complex numbers, 4-6
equation of a straight line, 4-7
ebraic and arithmetic operations
 objects, 5-1
 with algebraic objects, 5-2
e ALG menu , 5-3
anscendental functions, 5-5
d factoring using log-exp functions, 5-5
d factoring using trigonometric functions, 5-6
RITHMETIC menu, 5-7
 function, 5-8
X, 5-8
nction, 5-8
The PROOT function, 5-9
The QUOT and REMAINDER functions, 5-9
The PEVAL function , 5-9
Fractions, 5-9
The SIMP2 function, 5-10
The PROPFRAC function, 5-10
The PARTFRAC
The FCOEF fu
The FROOTS 
Step-by-step oper
Reference, 5-12
Chapter 6 - Sol
Symbolic solution 
Function ISOL
Function SOLV
Function SOLV
Function ZERO
Numerical solver 
Polynomial Eq
Finding the
Generating
6-7
Generating
Financial calc
Solving equat
Function ST
Solution to simulta
Reference, 6-11
Chapter 7 - Op
Creating and stori
Operations with li
Changing sign
SG49A.book Page 4 Friday, September 16, 2005 1:31 PM
Page TOC-4
 function, 5-10
nction, 5-10
function, 5-11
ations with polynomials and fractions, 5-11
ution to equations
of algebraic equations, 6-1
, 6-1
E, 6-2
EVX, 6-4
S, 6-4
menu, 6-5
uations, 6-6
 solutions to a polynomial equation, 6-6
 polynomial coefficients given the polynomial's roots, 
 an algebraic expression for the polynomial, 6-8
ulations, 6-8
ions with one unknown through NUM.SLV, 6-9
EQ, 6-9
neous equations with MSLV, 6-10
erations with lists
ng lists, 7-1
sts of numbers, 7-1
 , 7-1
Page TOC-5
Addition, subtraction, multiplication, division, 7-2
Functions applied to lists, 7-4
Lists of complex numbers, 7-4
Lists of algebraic objects, 7-5
The MTH/LIST menu, 7-5
The SEQ function, 7-7
The MAP function,
Reference, 7-7
Chapter 8 - Vec
Entering vectors, 
Typing vectors
Storing vector
Using the Mat
Simple operations
Changing sig
Addition, subt
Multiplication
Absolute value
The MTH/VECTOR
Magnitude, 8
Dot product , 
Cross product
Reference, 8-8
Chapter 9 - Ma
Entering matrices 
Using the Mat
Typing in the 
Operations with m
Addition and 
Multiplication,
Multiplicati
Matrix-vect
SG49A.book Page 5 Friday, September 16, 2005 1:31 PM
 7-7
tors
8-1
 in the stack, 8-1
s into variables in the stack, 8-2
rix Writer (MTRW) to enter vectors, 8-3
 with vectors, 8-5
n, 8-5
raction, 8-5
 by a scalar, and division by a scalar, 8-6
 function, 8-6
 menu, 8-6
-7
8-7
, 8-7
trices and linear algebra
in the stack, 9-1
rix Writer, 9-1
matrix directly into the stack, 9-2
atrices, 9-3
subtraction, 9-4
 9-4
on by a scalar, 9-4
or multiplication, 9-5
Matrix multiplication, 9-5
Term-by-term multiplication, 9-6
Raising a matrix to a real power, 9-6
The identity matrix, 9-7
The inverse matrix, 9-7
Characterizing a matrix (The matrix NORM menu), 9-8
Function DET,
Function TRAC
Solution of linear 
Using the num
Solution with t
Solution by “d
References, 9-12
Chapter 10 - G
Graphs options in
Plotting an expres
Generating a tabl
Fast 3D plots, 10-
Reference, 10-7
Chapter 11 - Ca
The CALC (Calculu
Limits and derivat
Function lim, 1
Functions DER
Anti-derivatives a
Functions INT,
Definite integr
Infinite series, 11-
Functions TAY
Reference, 11-6
SG49A.book Page 6 Friday, September 16, 2005 1:31 PM
Page TOC-6
 9-8
E, 9-8
systems, 9-9
erical solver for linear systems, 9-9
he inverse matrix, 9-11
ivision” of matrices, 9-11
raphics
 the calculator, 10-1
sion of the form y = f(x), 10-2
e of values for a function, 10-4
5
lculus Applications
s) menu, 11-1
ives, 11-1
1-1
IV and DERVX, 11-3
nd integrals, 11-3
 INTVX, RISCH, SIGMA and SIGMAVX, 11-3
als, 11-4
5
LR, TAYLR0, and SERIES, 11-5
Page TOC-7
Chapter 12 - Multi-variate Calculus Applications
Partial derivatives, 12-1
Multiple integrals, 12-2
Reference, 12-2
Chapter 13 - Vector Analysis Applications
The del operator, 
Gradient, 13-1
Divergence, 13-2
Curl, 13-2
Reference, 13-2
Chapter 14 - D
The CALC/DIFF me
Solution to linear 
Function LDEC
Function DESO
The variable O
Laplace Transform
Laplace transf
Fourier series, 14
Function FOU
Fourier series 
Reference, 14-7
Chapter 15 - Pr
The MTH/PROBAB
Factorials, com
Random numb
The MTH/PROB m
The Normal d
The Student-t d
The Chi-squar
The F distribut
SG49A.book Page 7 Friday, September 16, 2005 1:31 PM
13-1
ifferential Equations 
nu, 14-1
and non-linear equations, 14-1
, 14-1
LVE, 14-3
DETYPE, 14-3
s, 14-4
orm and inverses in the calculator, 14-4
-5
RIER, 14-5
for a quadratic function, 14-6
obability Distributions
ILITY.. sub-menu - part 1, 15-1
binations, and permutations, 15-1
ers, 15-2
enu - part 2, 15-3
istribution, 15-3
istribution, 15-3
e distribution, 15-4
ion, 15-4
Reference, 15-4
Chapter 16 - Statistical Applications
Entering data, 16-1
Calculating single-variable statistics, 16-2
Sample vs. population, 16-2
Obtaining frequen
Fitting data to a fu
Obtaining additio
Confidence interva
Hypothesis testing
Reference, 16-11
Chapter 17 - N
The BASE menu, 1
Writing non-decim
Reference, 17-2
Chapter 18 - U
Inserting and rem
Formatting an SD 
Accessing objects 
Storing objects on
Recalling an objec
Purging an object
Purging all objects
Specifying a direc
Chapter 19 - Eq
Reference, 19-4
Limited Warranty,
Service, W-3
Regulatory inform
Disposal of Waste
ropean Union, W
SG49A.book Page 8 Friday, September 16, 2005 1:31 PM
Page TOC-8
cy distributions, 16-3
nction y = f(x), 16-5
nal summary statistics, 16-6
ls, 16-7
, 16-9
umbers in Different Bases
7-1
al numbers, 17-2
sing SD cards
oving an SD card, 18-1
card, 18-1
on an SD card, 18-2
 the SD card, 18-2
t from the SD card, 18-3
 from the SD card, 18-3
 on the SD card (by reformatting), 18-4
tory on an SD card, 18-4
uation Library
 W-1
ation, W-5
 Equipment by Users in Private Household in the Eu-
-7
Page 1-1
Chapter 1
Getting started
This chapter provides basic information about the operation of your 
calculator. It is designed to familiarize you with the basic operations and 
settings before you perform a calculation.
Basic Operati
Batteries
The calculator uses 4
lithium battery for me
Before using the calc
following procedure.
To install the main b
a. Make sure the cal
cover as illustrated
b. Insert 4 new AAA
sure each battery 
To install the back
a. Make sure the cal
to the shown direc
SG49A.book Page 1 Friday, September 16, 2005 1:31 PM
ons
 AAA (LR03) batteries as main power and a CR2032 
mory backup.
ulator, please install the batteries according to the 
atteries 
culator is OFF. Slide up the battery compartment 
.
 (LR03) batteries into the main compartment. Make 
is inserted in the indicated direction.
up battery
culator is OFF. Press down the holder. Push the plate 
tion and lift it.
b. Insert a new CR20
facing up.
c. Replace the plate 
After installing the ba
Warning: When the l
batteries as soon as p
and main batteries at
Turning the calc
The $ key is locat
once to turn your cal
shift key @ (first key
followed by the $ k
in the upper right cor
Adjusting the d
You can adjust the di
the + or - keys.
The $(hold) + k
The $(hold) - k
Page 1-2
32 lithium battery. Make sure its positive (+) side is 
and push it to the original place.
tteries, press $ to turn the power on.
ow battery icon is displayed, you need to replace the 
ossible. However, avoid removing the backup battery 
 the same time to avoid data lost.
ulator on and off
ed at the lower left corner of the keyboard. Press it 
culator on. To turn the calculator off, press the right-
 in the second row from the bottom of the keyboard), 
ey. Notice that the $ key has a OFF label printed 
ner as a reminder of the OFF command.
isplay contrast
splay contrast by holding the $ key while pressing 
ey combination produces a darker display
ey combination produces a lighter display
Page 1-3
Contents of the calculator’s display
Turn your calculator on once more. At the top of the display you will have 
two lines of information that describe the settings of the calculator. The first 
line shows the characters:
RAD XYZ HEX R= 'X'
For details on the meaning of these symbols see Chapter 2 in the 
calculator’s user’s gu
The second line show
indicating that the H
calculator’s memory.
At the bottom of the d
@E
associated with the si
The six labels displa
depending on whic
associated with the f
label, and so on.
Menus
The six labels associa
menu of functions. S
display 6 labels at a
than six entries. Each
to the next menu pag
key is the third key fro
The TOOL menu
The soft menu keys f
associated with ope
section on variables i
@EDIT A EDIT the
and Cha
informat
@VIEW B VIEW th
SG49A.book Page 3 Friday, September 16, 2005 1:31 PM
ide. 
s the characters
{ HOME }
OME directory is the current file directory in the 
isplay you will find a number of labels, namely,
DIT @VIEW @@RCL@@ @@STO@ !PURGE !CLEAR
x soft menu keys, F1 through F6:
ABCDEF
yed in the lower part of the screen will change 
h menu is displayed. But A will always be 
irst displayed label, B with the second displayed 
ted with the keys A through F form part of a 
ince the calculator has only six soft menu keys, it only 
ny point in time. However, a menu can have more 
 group of 6 entries is called a Menu page. To move 
e (if available), press the L (NeXT menu) key. This 
m the left in the third row of keys in the keyboard.
or the default menu,known as the TOOL menu, are 
rations related to manipulation of variables (see 
n this Chapter):
 contents of a variable (see Chapter 2 in this guide 
pter 2 and Appendix L in the user’s guide for more 
ion on editing)
e contents of a variable
These six functions form the first page of the TOOL menu. This menu has 
actually eight entries arranged in two pages. The second page is 
available by pressing
from the left in the thi
In this case, only the
with them. These com
Pressing the L key
recover the TOOL me
the second row of key
Setting time and
See Chapter 1 in the 
date.
Introducing th
The figure on the nex
with the numbering o
five functions. The m
label in the key. Als
(9,1), and the ALPHA
other keys to activate 
@@RCL@ C ReCaLl the contents of a variable
@@STO@ D STOre the contents of a variable
!PURGE E PURGE a variable
@CLEAR F CLEAR the display or stack
@CASCM A CASCM
the CAS
@HELP B HELP fac
calculato
Page 1-4
 the L (NeXT menu) key. This key is the third key 
rd row of keys in the keyboard.
 first two soft menu keys have commands associated 
mands are:
 will show the original TOOL menu. Another way to 
nu is to press the I key (third key from the left in 
s from the top of the keyboard).
 date
calculator’s user’s guide to learn how to set time and 
e calculator’s keyboard
t page shows a diagram of the calculator’s keyboard 
f its rows and columns. Each key has three, four, or 
ain key function correspond to the most prominent 
o, the left-shift key, key (8,1), the right-shift key, key 
 key, key (7,1), can be combined with some of the 
the alternative functions shown in the keyboard.
D: CAS CoMmanD, used to launch a command from 
 (Computer Algebraic System) by selecting from a list
ility describing the commands available in the 
r
Page 1-5
For example, the P
associated with it:
P Main
„´ Left-s
…N Righ
~p ALPH
~„p ALPH
SG49A.book Page 5 Friday, September 16, 2005 1:31 PM
 key, key(4,4), has the following six functions 
 function, to activate the SYMBolic menu
hift function, to activate the MTH (Math) menu
t-shift function, to activate the CATalog function
A function, to enter the upper-case letter P
A-Left-Shift function, to enter the lower-case letter p
Of the six functions associated with a key only the first four are shown in 
the keyboard itself. The figure in next page shows these four labels for the 
P key. Notice that the color and the position of the labels in the key, 
namely, SYMB, MTH, CAT and P, indicate which is the main function 
(SYMB), and which of the other three functions is associated with the left-
shift „(MTH), right-shift …(CAT ), and ~ (P) keys.
For detailed informa
Appendix B in the ca
Selecting calc
This section assumes 
use of choose and dia
in the user’s guide).
Press the H button
from the top) to show
Press the !!@@OK#@ soft m
selecting different cal
~…p ALPHA-Right-Shift function, to enter the symbol π
Page 1-6
tion on the calculator keyboard operation refer to 
lculator’s user’s guide.
ulator modes
that you are now at least partially familiar with the 
log boxes (if you are not, please refer to appendix A 
 (second key from the left on the second row of keys 
 the following CALCULATOR MODES input form:
enu key to return to normal display. Examples of 
culator modes are shown next.
Page 1-7
Operating Mode
The calculator offers two operating modes: the Algebraic mode, and the 
Reverse Polish Notation (RPN) mode. The default mode is the Algebraic 
mode (as indicated in the figure above), however, users of earlier HP 
calculators may be more familiar with the RPN mode.
To select an operating mode, first open the CALCULATOR MODES input 
form by pressing the H button. The Operating Mode field will be 
highlighted. Select th
the \ key (second 
pressing the @CHOOS so
down arrow keys, —
menu key to complete
To illustrate the diffe
calculate the followin
To enter this express
writer, ‚O. P
besides the numeric k
!
Q¸
The equation writer
mathematical expres
fractions, derivatives,
writing the expression
‚O
1
/23.
After pressing ` th
√ (3.*(
Pressing ` again w
on, if asked, by press
SG49A.book Page 7 Friday, September 16, 2005 1:31 PM
e Algebraic or RPN operating mode by either using 
from left in the fifth row from the keyboard bottom), or 
ft menu key. If using the latter approach, use up and 
 ˜, to select the mode, and press the !!@@OK#@ soft 
 the operation. 
rence between these two operating modes we will 
g expression in both modes:
ion in the calculator we will first use the equation 
lease identify the following keys in the keyboard, 
eypad keys:
@.#*+-/R
Ü‚Oš™˜—`
 is a display mode in which you can build 
sions using explicit mathematical notation including 
 integrals, roots, etc. To use the equation writer for 
 shown above, use the following keystrokes:
R3.*!Ü5.-
./3.*3.
—————
Q3™™+!¸2.5`
e calculator displays the expression:
5.-1/(3.*3.))/23.^3+EXP(2.5))
ill provide the following value (accept Approx mode 
ing !!@@OK#@):
5.2
3
0.23
0.30.3
1
0.50.3
e+
⋅
−⋅ ⎟
⎠
⎞
⎜
⎝
⎛
You could also type the expression directly into the display without using 
the equation writer, a
R!
1
/23
to obtain the same re
Change the operatin
Select the RPN opera
the @CHOOS soft menu 
operation. The displa
Notice that the displa
to top, as 1, 2, 3, etc
different levels are re
level 2, etc.
What RPN means is t
pressing
we write the operand
As you enter the op
3` puts the nu
the 3 upwards to occ
telling the calculator 
levels 1 and 2. The r
SG49A.book Page 8 Friday, September 16, 2005 1:31 PM
Page 1-8
s follows:
Ü3.*!Ü5.-
/3.*3.™
.Q3+!¸2.5`
sult.
g mode to RPN by first pressing the H button. 
ting mode by either using the \ key, or pressing 
key. Press the @@OK#@ soft menu key to complete the 
y, for the RPN mode looks as follows:
y shows several levels of output labeled, from bottom 
. This is referred to as the stack of the calculator. The 
ferred to as the stack levels, i.e., stack level 1, stack 
hat, instead of writing an operation such as 3 + 2 by 
3+2`
s first, in the proper order, and then the operator, i.e., 
3`2+
erands, they occupy different stack levels. Entering 
mber 3 in stack level 1. Next, entering 2 pushes 
upy stack level 2. Finally, by pressing +, we are 
to apply the operator, +, to the objects occupying 
esult, 5, is then placed in level 1.
Page 1-9
Let's try some other simple operations before trying the more complicated 
expression used earlier for the algebraic operating mode:
Note the position of t
exponential operatio
level 1) before the 
operation, y (stack le
level 1) is the root.
Try the following exer
Let's try now the expr
123/32 123`32/
42 4`2Q
3√(√27) 27R3@»
5`3
2X
3` Ente
5` Ente
3` Ente
3* Plac
Y 1/(3
- 5 - 1
* 3 × 
23`Ente
3Q Ente
/ (3 ×
2.5Ente
!¸ e2.5,
SG49A.book Page 9 Friday, September 16, 2005 1:31 PM
he y and x in the last two operations. The base in the 
n is y (stack level 2) while the exponent is x (stack 
key Q is pressed. Similarly, in the cubic root 
vel 2) is the quantity under the root sign, and x (stack 
cise involving 3 factors: (5 + 3) × 2
ession proposed earlier:
+ Calculates (5 +3) first.
Completes the calculation.
r 3 in level 1
r 5 in level 1, 3 moves to level 2
r 3 in level 1, 5 moves to level 2, 3 to level 3
e 3 and multiply, 9 appears in level 1
×3), last value in lev. 1; 5 in level 2; 3 in level 3
/(3×3) , occupies level 1 now; 3 in level 2
(5 - 1/(3×3)), occupies level 1 now.
r 23 in level 1, 14.66666 moves to level 2.
r 3, calculate 233 into level 1. 14.666 in lev. 2.
 (5-1/(3×3)))/233 into level1
r 2.5 level 1
 goes into level 1, level 2 shows previous value.
5.2
3
23
33
1
53
e+
⋅
−⋅ ⎟
⎠
⎞
⎜
⎝
⎛
To select between the ALG vs. RPN operating mode, you can also set/
clear system flag 95 through the following keystroke sequence:
H @FLAGS! 9˜˜˜˜ `
Number Forma
Changing the numb
numbers are displa
extremely useful in op
decimals in a result.
To select a number fo
by pressing the H 
the option Number fo
the standard format, 
no set decimal placem
calculator (12 signific
in this guide. To illus
exercises:
Standard format
This mode is the mos
notation. Press the !!@@O
to return to the calcula
(with16 significant fig
the maximum 12 sign
Fixed format with
Press the H button
option Number form
option Fixed with the 
+ (3 × (5 - 1/(3 × 3)))/233 + e
2.5 = 12.18369, into lev. 1.
R √((3 × (5 - 1/(3×3)))/233 + e2.5) = 3.4905156, into 1.
SG49A.book Page 10 Friday, September 16, 2005 1:31 PM
Page 1-10
t and decimal dot or comma
er format allows you to customize the way real 
yed by the calculator. You will find this feature 
erations with powers of tens or to limit the number of 
rmat, first open the CALCULATOR MODES input form 
button. Then, use the down arrow key, ˜, to select 
rmat. The default value is Std, or Standard format. In 
the calculator will show floating-point numbers with 
ent and with the maximum precision allowed by the 
ant digits).”To learn more about reals, see Chapter 2 
trate this and other number formats try the following 
t used mode as it shows numbers in the most familiar 
K#@ soft menu key, with the Number format set to Std, 
tor display. Enter the number 123.4567890123456 
ures). Press the ` key. The number is rounded to 
ificant figures, and is displayed as follows:
 decimals
. Next, use the down arrow key, ˜, to select the 
at. Press the @CHOOS soft menu key, and select the 
arrow down key ˜.
Page 1-11
Press the right arrow
Fix. Press the @CHOOS
keys, —˜, select,
Press the !!@@OK#@ soft m
Press the !!@@OK#@ soft m
now is shown as:
Notice how the num
123.456789012345
as 123.456 because
Scientific format
To set this format, sta
arrow key, ˜, to se
menu key, and selec
SG49A.book Page 11 Friday, September 16, 2005 1:31 PM
 key, ™, to highlight the zero in front of the option 
 soft menu key and, using the up and down arrow 
 say, 3 decimals.
enu key to complete the selection:
enu key return to the calculator display. The number 
ber is rounded, not truncated. Thus, the number 
6, for this setting, is displayed as 123.457, and not 
 the digit after 6 is > 5. 
rt by pressing the H button. Next, use the down 
lect the option Number format. Press the @CHOOS soft 
t the option Scientific with the arrow down key ˜. 
Keep the number 3 in front of the Sci. (This number can be changed in the 
same fashion that we changed the Fixed number of decimals in the 
example above).
Press the !!@@OK#@ soft m
now is shown as:
This result, 1.23E2, 
i.e., 1.235 × 102. In
front of the Sci numb
significant figures af
includes one integer 
number of significant
Engineering forma
The engineering form
the powers of ten are
the H button. Nex
Number format. Pre
Engineering with the 
the Eng. (This num
changed the Fixed nu
SG49A.book Page 12 Friday, September 16, 2005 1:31 PM
Page 1-12
enu key return to the calculator display. The number 
is the calculator’s version of powers-of-ten notation, 
 this, so-called, scientific notation, the number 3 in 
er format (shown earlier) represents the number of 
ter the decimal point. Scientific notation always 
figure as shown above. For this case, therefore, the 
 figures is four.
t
at is very similar to the scientific format, except that 
 multiples of three. To set this format, start by pressing 
t, use the down arrow key, ˜, to select the option 
ss the @CHOOS soft menu key, and select the option 
arrow down key ˜. Keep the number 3 in front of 
ber can be changed in the same fashion that we 
mber of decimals in an earlier example). 
Page 1-13
Press the !!@@OK#@ soft menu key return to the calculator display. The number 
now is shown as:
Because this number has three figures in the integer part, it is shown with 
four significative fig
Engineering format. 
Decimal comma v
Decimal points in flo
the user is more fami
commas, change the 
commas, as follows (
Std):
Press the H button.
right arrow key, ™,
press the soft m
Press the !!@@OK#@ soft m
123.456789012345
SG49A.book Page 13 Friday, September 16, 2005 1:31 PM
ures and a zero power of ten, while using the 
For example, the number 0.00256, will be shown as:
s. decimal point
ating-point numbers can be replaced by commas, if 
liar with such notation. To replace decimal points for 
FM option in the CALCULATOR MODES input form to 
Notice that we have changed the Number Format to 
 Next, use the down arrow key, ˜, once, and the 
 highlighting the option __FM,. To select commas, 
enu key. The input form will look as follows:
enu key return to the calculator display. The number 
6, entered earlier, now is shown as:
Angle Measure
Trigonometric functions, for example, require arguments representing plane 
angles. The calculator provides three different Angle Measure modes for 
working with angles, namely:
• Degrees: There are 360 degrees (360°) in a complete circumference.
• Radians: There are 2π radians (2π r) in a complete circumference.
• Grades: There are
The angle measure 
associated functions.
To change the angle 
• Press the H butt
Select the Angle M
from left in the fifth
@CHOOS soft menu k
arrow keys, —˜
soft menu key to c
screen, the Radian
Coordinate Sys
The coordinate syste
numbers are displa
numbers and vectors
There are three coord
(RECT), Cylindrical 
coordinate system:
• Press the H butt
Select the Coord S
from left in the fifth
@CHOOS soft menu k
arrow keys, —˜
SG49A.book Page 14 Friday, September 16, 2005 1:31 PM
Page 1-14
 400 grades (400 g) in a complete circumference.
affects the trig functions like SIN, COS, TAN and 
measure mode, use the following procedure:
on. Next, use the down arrow key, ˜, twice. 
easure mode by either using the \ key (second 
 row from the keyboard bottom), or pressing the 
ey. If using the latter approach, use up and down 
, to select the preferred mode, and press the !!@@OK#@ 
omplete the operation. For example, in the following 
s mode is selected:
tem
m selection affects the way vectors and complex 
yed and entered. To learn more about complex 
, see Chapters 4 and 8, respectively, in this guide. 
inate systems available in the calculator: Rectangular 
(CYLIN), and Spherical (SPHERE). To change 
on. Next, use the down arrow key, ˜, three times. 
ystem mode by either using the \ key (second 
 row from the keyboard bottom), or pressing the 
ey. If using the latter approach, use up and down 
, to select the preferred mode, and press the !!@@OK#@ 
Page 1-15
soft menu key to complete the operation. For example, in the following 
screen, the Polar coordinate mode is selected:
Selecting CAS
CAS stands for Comp
of the calculator w
functions are program
adjusted according to
CAS settings use the 
• Press the H but
• To change CAS se
values of the CAS
• To navigate throug
use the arrow keys
• To select or desele
underline before th
key until the right 
check mark will be
SG49A.book Page 15 Friday, September 16, 2005 1:31 PM
 settings
uter Algebraic System. This is the mathematical core 
here the symbolic mathematical operations and 
med. The CAS offers a number of settings can be 
 the type of operation of interest. To see the optional 
following:
ton to activate the CALCULATOR MODES input form. 
ttingspress the @@CAS@@ soft menu key. The default 
 setting are shown below:
h the many options in the CAS MODES input form, 
: š™˜—.
ct any of the settings shown above, select the 
e option of interest, and toggle the soft menu 
setting is achieved. When an option is selected, a 
 shown in the underline (e.g., the Rigorous and Simp 
Non-Rational options above). Unselected options will show no check 
mark in the underline preceding the option of interest (e.g., the 
_Numeric, _Approx, _Complex, _Verbose, _Step/Step, _Incr Pow 
options above).
• After having selected and unselected all the options that you want in 
the CAS MODES input form, press the @@@OK@@@ soft menu key. This will 
take you back to the CALCULATOR MODES input form. To return to 
normal calculator 
once more.
Explanation of 
• Indep var: The ind
VX = ‘X’.
• Modulo: For opera
modulus or modul
calculator’s user’s 
• Numeric: If set, th
result, in calculatio
numerically.
• Approx: If set, App
If unchecked, the C
results in algebrai
• Complex: If set, co
the CAS is in Real
See Chapter 4 for
• Verbose: If set, pro
operations.
• Step/Step: If set, p
operations. Usefu
integrals, polynom
operations.
• Incr Pow: Increasin
shown in increasin
• Rigorous: If set, ca
|X| to X.
• Simp Non-Rationa
expressions as mu
SG49A.book Page 16 Friday, September 16, 2005 1:31 PM
Page 1-16
display at this point, press the @@@OK@@@ soft menu key 
CAS settings
ependent variable for CAS applications. Typically, 
tions in modular arithmetic this variable holds the 
o of the arithmetic ring (see Chapter 5 in the 
guide).
e calculator produces a numeric, or floating-point 
ns. Note that constants will always be evaluated 
roximate mode uses numerical results in calculations. 
AS is in Exact mode, which produces symbolic 
c calculations.
mplex number operations are active. If unchecked 
 mode, i.e., real number calculations are the default. 
 operations with complex numbers.
vides detailed information in certain CAS 
rovides step-by-step results for certain CAS 
l to see intermediate steps in summations, derivatives, 
ial operations (e.g., synthetic division), and matrix 
g Power, means that, if set, polynomial terms are 
g order of the powers of the independent variable.
lculator does not simplify the absolute value function 
l: If set, the calculator will try to simplify non-rational 
ch as possible.
Page 1-17
Selecting Display modes
The calculator display can be customized to your preference by selecting 
different display modes. To see the optional display settings use the 
following:
• First, press the H button to activate the CALCULATOR MODES input 
form. Within the CALCULATOR MODES input form, press the @@DISP@ 
soft menu key to d
• To navigate throug
form, use the arrow
• To select or desele
check mark, selec
toggle the 
When an option i
underline (e.g., th
Unselected option
the option of inter
in the Edit: line ab
• To select the Font 
option in the DISP
• After having selec
the DISPLAY MOD
take you back to t
normal calculator 
once more.
SG49A.book Page 17 Friday, September 16, 2005 1:31 PM
isplay the DISPLAY MODES input form.
h the many options in the DISPLAY MODES input 
 keys: š™˜—.
ct any of the settings shown above, that require a 
t the underline before the option of interest, and 
soft menu key until the right setting is achieved. 
s selected, a check mark will be shown in the 
e Textbook option in the Stack: line above). 
s will show no check mark in the underline preceding 
est (e.g., the _Small, _Full page, and _Indent options 
ove).
for the display, highlight the field in front of the Font: 
LAY MODES input form, and use the @CHOOS soft menu.
ted and unselected all the options that you want in 
ES input form, press the @@@OK@@@ soft menu key. This will 
he CALCULATOR MODES input form. To return to 
display at this point, press the @@@OK@@@ soft menu key 
Selecting the display font
First, press the H button to activate the CALCULATOR MODES input 
form. Within the CALCULATOR MODES input form, press the @@DISP@ soft 
menu key to display the DISPLAY MODES input form. The Font: field is 
highlighted, and the option Ft8_0: system 8 is selected. This is the default 
value of the display font. Pressing the @CHOOS soft menu key will provide a 
list of available system fonts, as shown below:
The options available
and a Browse.. opt
memory for addition
into the calculator.
Practice changing th
menu key to effect th
the @@@OK@@@ soft menu 
form. To return to no
soft menu key once
accommodate the dif
Selecting prope
First, press the H 
form. Within the CA
menu key to display
arrow key, ˜, on
properties that can 
(checked) the followin
Instructions on the use
user’s guide.
_Small Chan
_Full page Allow
_Indent Auto
SG49A.book Page 18 Friday, September 16, 2005 1:31 PM
Page 1-18
 are three standard System Fonts (sizes 8, 7, and 6) 
ion. The latter will let you browse the calculator 
al fonts that you may have created or downloaded 
e display fonts to sizes 7 and 6. Press the OK soft 
e selection. When done with a font selection, press 
key to go back to the CALCULATOR MODES input 
rmal calculator display at this point, press the @@@OK@@@
 more and see how the stack display change to 
ferent font.
rties of the line editor
button to activate the CALCULATOR MODES input 
LCULATOR MODES input form, press the @@DISP@ soft 
 the DISPLAY MODES input form. Press the down 
ce, to get to the Edit line. This line shows three 
be modified. When these properties are selected 
g effects are activated:
 of the line editor are presented in Chapter 2 in the 
ges font size to small
s to place the cursor after the end of the line
 indent cursor when entering a carriage return
Page 1-19
Selecting properties of the Stack
First, press the H button to activate the CALCULATOR MODES input 
form. Within the CALCULATOR MODES input form, press the @@DISP@ soft 
menu key (D) to display the DISPLAY MODES input form. Press the 
down arrow key, ˜, twice, to get to the Stack line. This line shows two 
properties that can be modified. When these properties are selected 
(checked) the following effects are activated:
To illustrate these se
equation writer to typ
‚O…Á
In Algebraic mode, th
with neither _Small n
With the _Small optio
With the _Textbook o
the _Small option is s
_Small Chan
infor
overr
 _Textbook Disp
math
SG49A.book Page 19 Friday, September 16, 2005 1:31 PM
ttings, either in algebraic or RPN mode, use the 
e the following definite integral:
0™„虄¸\x™x`
e following screen shows the result of these keystrokes 
or _Textbook are selected:
n selected only, the display looks as shown below:
ption selected (default value), regardless of whether 
elected or not, the display shows the following result:
ges font size to small. This maximizes the amount of 
mation displayed on the screen. Note, this selection 
ides the font selection for the stack display.
lays mathematical expressions in graphical 
ematical notation
Selecting properties of the equation writer (EQW)
First, press the H button to activate the CALCULATOR MODES input 
form. Within the CALCULATOR MODES input form, press the @@DISP@ soft 
menu key to display the DISPLAY MODES input form. Press the down 
arrow key, ˜, three times, to get to the EQW (Equation Writer) line. This 
line shows two properties that can be modified. When these properties 
are selected (checked) the following effects are activated:
Detailed instructions 
presented elsewhere 
For the example of th
_Small Stack Disp in
produces the followin
References
Additional references
in Chapter 1 and Ap
_Small C
e
_Small Stack Disp S
e
SG49A.book Page20 Friday, September 16, 2005 1:31 PM
Page 1-20
on the use of the equation editor (EQW) are 
in this manual.
e integral , presented above, selecting the 
 the EQW line of the DISPLAY MODES input form 
g display:
 on the subjects covered in this Chapter can be found 
pendix C of the calculator’s user’s guide. 
hanges font size to small while using the equation 
ditor
hows small font in the stack after using the equation 
ditor
∫
∞
−
0
dXe
X
Page 2-1
Chapter 2
Introducing the calculator
In this chapter we present a number of basic operations of the calculator 
including the use of the Equation Writer and the manipulation of data 
objects in the calculator. Study the examples in this chapter to get a good 
grasp of the capabilities of the calculator for future applications.
Calculator ob
Some of the most com
with a decimal poin
written without a d
numbers (written as 
objects are described
Editing expre
In this section we pre
calculator display or 
Creating arithm
For this example, we 
format with 3 decim
arithmetic expression
To enter this expressio
5.*„
„Ü
The resulting expressi
Press ` to get the 
SG49A.book Page 1 Friday, September 16, 2005 1:31 PM
jects
monly used objects are: reals (real numbers, written 
t, e.g., -0.0023, 3.56), integers (integer numbers, 
ecimal point, e.g., 1232, -123212123), complex 
an ordered pair, e.g., (3,-2)), lists, etc. Calculator 
 in Chapters 2 and 24 in the calculator’s user guide.
ssions in the stack
sent examples of expression editing directly into the 
stack.
etic expressions
select the Algebraic operating mode and select a Fix
als for the display. We are going to enter the 
:
n use the following keystrokes:
Ü1.+1/7.5™/
R3.-2.Q3
on is: 5*(1+1/7.5)/( √3-2^3). 
expression in the display as follows:
3
0.20.3
5.7
0.1
0.1
0.5
−
+
⋅
Notice that, if your CAS is set to EXACT (see Appendix C in user’s guide) 
and you enter your e
the result is a symboli
5*„
„
Before producing a r
mode. Accept the ch
mode with three deci
In this case, when the
as you press `, th
expression. If the e
calculator will reprod
³5*„
„
The result will be show
To evaluate the expre
SG49A.book Page 2 Friday, September 16, 2005 1:31 PM
Page 2-2
xpression using integer numbers for integer values, 
c quantity, e.g.,
Ü1+1/7.5™/
ÜR3-2Q3
esult, you will be asked to change to Approximate 
ange to get the following result (shown in Fix decimal 
mal places – see Chapter 1):
 expression is entered directly into the stack, as soon 
e calculator will attempt to calculate a value for the 
xpression is preceded by a tickmark, however, the 
uce the expression as entered. For example:
Ü1+1/7.5™/
ÜR3-2Q3`
n as follows:
ssion we can use the EVAL function, as follows:
µ„î`
Page 2-3
If the CAS is set to Exact, you will be asked to approve changing the CAS 
setting to Approx. Once this is done, you will get the same result as 
before.
An alternative way to evaluate the expression entered earlier between 
quotes is by using the option …ï.
We will now enter the expression used above when the calculator is set to 
the RPN operating mode. We also set the CAS to Exact, the display to 
Textbook, and the nu
expression between q
³5*„
„
Resulting in the outpu
Press ` once more
stack for evaluation. 
µ
This expression is se
components to the re
[using ™] and evalu
This latter result is p
although representing
they are not, we subt
function EVAL: -µ
For additional inform
or stack, see Chapter
SG49A.book Page 3 Friday, September 16, 2005 1:31 PM
mber format to Standard. The keystrokes to enter the 
uotes are the same used earlier, i.e.,
Ü1+1/7.5™/
ÜR3-2Q3`
t
 to keep two copies of the expression available in the 
We first evaluate the expression by pressing:
!î` or @ï`
mi-symbolic in the sense that there are floating-point 
sult, as well as a √3. Next, we switch stack locations 
ate using function �NUM, i.e., ™…ï.
urely numerical, so that the two results in the stack, 
 the same expression, seem different. To verify that 
ract the two values and evaluate this difference using 
. The result is zero (0.).
ation on editing arithmetic expressions in the display 
 2 in the calculator’s user’s guide.
Creating algebraic expressions
Algebraic expressions include not only numbers, but also variable names. 
As an example, we will enter the following algebraic expression:
We set the calculator
the display to Textbo
following keystrokes:
³2*~
~r™/„Ü
Press ` to get the f
Entering this express
exactly the same as th
For additional infor
calculator’s display o
LR
x
L
2
12
+
+
SG49A.book Page 4 Friday, September 16, 2005 1:31 PM
Page 2-4
 operating mode to Algebraic, the CAS to Exact, and 
ok. To enter this algebraic expression we use the 
l*R„Ü1+~„x/
~r+~„y™+2*~l/
~„b
ollowing result:
ion when the calculator is set in the RPN mode is 
is Algebraic mode exercise.
mation on editing algebraic expressions in the 
r stack see Chapter 2 in the calculator’s user’s guide.
byR +
Page 2-5
Using the Equation Writer (EQW) to create 
expressions
The equation writer is an extremely powerful tool that not only let you enter 
or see an equation, but also allows you to modify and work/apply 
functions on all or part of the equation.
The Equation Writer is launched by pressing the keystroke combination 
‚O (the third ke
resulting screen is the
The six soft menu ke
CURS, BIG, EVAL, 
information on these 
user’s guide.
Creating arithm
Entering arithmetic e
entering an arithmet
main difference is tha
written in “textbook” 
following keystrokes i
The result is the expre
The cursor is shown 
edition location. Fo
above, type now:
*
The edited expression
SG49A.book Page 5 Friday, September 16, 2005 1:31 PM
y in the fourth row from the top in the keyboard). The 
 following. Press L to see the second menu page:
 
ys for the Equation Writer activate functions EDIT, 
FACTOR, SIMPLIFY, CMDS, and HELP. Detailed 
functions is provided in Chapter 3 of the calculator’s 
etic expressions
xpressions in the Equation Writer is very similar to 
ic expression in the stack enclosed in quotes. The 
t in the Equation Writer the expressions produced are 
style instead of a line-entry style. For example, try the 
n the Equation Writer screen: 5/5+2
ssion:
as a left-facing key. The cursor indicates the current 
r example, for the cursor in the location indicated 
„Ü5+1/3
 looks as follows:
Suppose that you want to replace the quantity between parentheses in the 
denominator (i.e., 5+
(ƒ) delete the curre
with π2/2, as follows
When hit this point th
In order to insert the d
the entire π2 expressi
once. At that point, w
The expression now lo
Suppose that now 
expression, i.e., you w
SG49A.book Page 6 Friday, September 16, 2005 1:31 PM
Page 2-6
1/3) with (5+π2/2). First, we use the delete key 
nt 1/3 expression, and then we replace that fraction 
:
ƒƒƒ„ìQ2
e screen looks as follows:
enominator 2 in the expression, we need to highlight 
on. We do this by pressing the right arrow key (™) 
e enter the following keystrokes:
/2
oks as follows:
you want to add the fraction 1/3 to this entire 
ant to enter the expression:
3
1
)
2
5(25
5
2
+
+⋅+
π
Page 2-7
First, we need to highlight the entire first term by using either the right 
arrow (™) or the upper arrow (—) keys, repeatedly, until the entire 
expression is highlighted, i.e., seven times, producing:
Once the expression
3 to add the fracti
Creating algebr
An algebraic express
that English and Gre
an algebraic expres
creating an arithme
keyboard is included.
Toillustrate the use o
we will use the follo
expression:
Use the following key
2/R3™
™™*‚¹
NOTE: Alternative
right of the 2 in th
combination ‚—
SG49A.book Page 7 Friday, September 16, 2005 1:31 PM
 is highlighted as shown above, type +1/
on 1/3. Resulting in:
aic expressions
ion is very similar to an arithmetic expression, except 
ek letters may be included. The process of creating 
sion, therefore, follows the same idea as that of 
tic expression, except that use of the alphabetic 
 
f the Equation Writer to enter an algebraic equation 
wing example. Suppose that we want to enter the 
strokes:
™*~‚n+„¸\~‚m
~„x+2*~‚m*~‚c
ly, from the original position of the cursor (to the 
e denominator of π2/2), we can use the keystroke 
, interpreted as (‚ ‘ ).
⎟
⎠
⎞
⎜
⎝
⎛ ∆⋅+
⋅+ −
3/1
2
3
2
θ
µλ µ yxLNe
~„y———/~‚tQ1/3
This results in the output:
In this example we
(~„x), severa
combination of 
(~‚c~„y
letter, you need to use
want to enter. Also, 
CHARS menu (…±
combination that pro
keystroke combination
For additional info
simplifying algebraic
guide.
Organizing d
You can organize d
directory tree. The b
directory described n
The HOME dire
To get to the HOME d
as needed -- until the
display header. Alte
HOME directory cont
the variables in the so
SG49A.book Page 8 Friday, September 16, 2005 1:31 PM
Page 2-8
 used several lower-case English letters, e.g., x 
l Greek letters, e.g., λ(~‚n), and even a 
Greek and English letters, namely, ∆y
). Keep in mind that to enter a lower-case English 
 the combination: ~„ followed by the letter you 
you can always copy special characters by using the 
) if you don’t want to memorize the keystroke 
duces it. A listing of commonly used ~‚
s is listed in Appendix D of the user’s guide.
rmation on editing, evaluating, factoring, and 
 expressions see Chapter 2 of the calculator’s user’s 
ata in the calculator
ata in your calculator by storing variables in a 
asis of the calculator’s directory tree is the HOME 
ext.
ctory
irectory, press the UPDIR function („§) -- repeat 
 {HOME} spec is shown in the second line of the 
rnatively, use „ (hold) §. For this example, the 
ains nothing but the CASDIR. Pressing J will show 
ft menu keys:
Page 2-9
Subdirectories
To store your data in a well organized directory tree you may want to 
create subdirectories under the HOME directory, and more subdirectories 
within subdirectories, in a hierarchy of directories similar to folders in 
modern computers. The subdirectories will be given names that may reflect 
the contents of each subdirectory, or any arbitrary name that you can think 
off. For details on manipulation of directories see Chapter 2 in the 
calculator’s user’s gu
Variables
Variables are similar 
store one object (nu
matrices, programs, e
can be any combina
with a letter (either E
such as the arrow (→
an alphabetical chara
not. Valid examples
‘AB12’, ‘�A12’, ’Vel
A variable can not h
Some of the reserv
ALRMDAT, CST, EQ
PRTPAR, VPAR, ZPAR,
Variables can be or
calculator’s user’s gu
Typing variable
To name variables, y
may or may not be c
you can lock the alph
~~ locks the a
this fashion, pressing
letter, while pressing 
character. If the alph
lock it in lower case, 
~~„~ loc
locked in this fashion
upper case letter. To
SG49A.book Page 9 Friday, September 16, 2005 1:31 PM
ide.
to files on a computer hard drive. One variable can 
merical values, algebraic expressions, lists, vectors, 
tc). Variables are referred to by their names, which 
tion of alphabetic and numerical characters, starting 
nglish or Greek). Some non-alphabetic characters, 
) can be used in a variable name, if combined with 
cter. Thus, ‘→A’ is a valid variable name, but ‘→’ is 
 of variable names are: ‘A’, ‘B’, ‘a’, ‘b’, ‘α’, ‘β’, ‘A1’, 
’, ’Z0’, ’z1’, etc.
ave the same name as a function of the calculator. 
ed calculator variable names are the following: 
, EXPR, IERR, IOPAR, MAXR, MINR, PICT, PPAR, 
 der_, e, i, n1,n2, …, s1, s2, …, ΣDAT, ΣPAR, π, ∞.
ganized into sub-directories (see Chapter 2 in the 
ide).
 names 
ou will have to type strings of letters at once, which 
ombined with numbers. To type strings of characters 
abetic keyboard as follows:
lphabetic keyboard in upper case. When locked in 
 the „ before a letter key produces a lower case 
the ‚ key before a letter key produces a special 
abetic keyboard is already locked in upper case, to 
type, „~.
ks the alphabetic keyboard in lower case. When 
, pressing the „ before a letter key produces an 
 unlock lower case, press „~.
To unlock the upper-case locked keyboard, press ~.
Try the following exercises:
~~math`
~~m„a„t„h`
~~m„~at„h`
The calculator display will show the following (left-hand side is Algebraic 
mode, right-hand side
Creating variab
The simplest way to c
examples are used to
J if needed to see
Algebraic mode
To store the value of
~‚a. AT this p
Press ` to create 
menu key labels when
Name
α
A12
Q
R
z1
p1
SG49A.book Page 10 Friday, September 16, 2005 1:31 PM
Page 2-10
 is RPN mode):
 
les
reate a variable is by using the K. The following 
 store the variables listed in the following table (Press 
 variables menu):
 –0.25 into variable α: 0.25\K 
oint, the screen will look as follows:
the variable. The variable is now shown in the soft 
 you press J:
Contents Type
-0.25 real
3×105 real
‘r/(m+r)' algebraic
[3,2,1] vector
3+5i complex
 <<→ r 'π*r^2' >> program
Page 2-11
The following are the keystrokes for entering the remaining variables: 
A12: 3V5K~a12`
Q: ~„r/„
~„m+~„
R: „Ô3‚í
z1: 3+5*
Complex mode if ask
p1: å‚é~
~„rQ2™
The screen, at this po
You will see six of th
p1, z1, R, Q, A12, a
RPN mode
(Use H\@@OK@@ to
to store the value o
~‚a`. At t
With –0.25 on the le
you can use the K 
in the soft menu key l
Ü
r™™K~q`
2‚í1™K~r`
„¥K~„z1` (Accept change to
ed).
„r³„ì*
™™K~„p1`.
int, will look as follows:
e seven variables listed at the bottom of the screen:
.
 change to RPN mode). Use the following keystrokes
f –0.25 into variable α: .25\`³
his point, the screen will look as follows:
vel 2 of the stack and 'α' on the level 1 of the stack,
key to create the variable. The variable is now shown
abels when you press J:
To enter the value 3×105 into A12, we can use a shorter version of the 
procedure: 3V5³~a12`K
Here is a way to enter the contents of Q:
Q: ~„r/„
 ~„m+~„
To enter the value 
procedure:
R: „Ô3#2
Notice that to separa
the space key (#)
Algebraic mode. 
z1: ³3+5
p1: ‚å‚é
~„rQ2™
The screen, at this po
You will see six of th
p1, z1, R, Q, A12, α
SG49A.book Page 12 Friday, September 16, 2005 1:31 PM
Page 2-12
Ü
r™™³~q`K
of R, we can use an even shorter version of the 
#1™ ³~rK
te the elements of a vector in RPN mode we can use 
, rather than the comma (‚í) used above in 
*„¥³~„z1K
~„r³„ì*
™™³~„p1™`K.
int, will look as follows:
e seven variables listed at the bottom of the screen: 
.
Page 2-13
Checking variables contents
The simplest way to check a variable content is by pressing the soft menu 
key label for the variable. For example, for the variables listed above, 
press the following keys to see the contents of the variables:
Algebraic mode
Type these keystrokes: J@@z1@@ ` @@@R@@ `@@@Q@@@ `. At this point, the 
screen looks as follow
RPN mode
In RPN mode, you o
label to get the conte
under consideration, 
α, created above, as 
At this point, the scre
Using the right-sh
In Algebraic mode, y
J@ and then t
examples:
J‚@
NOTE: In RPN mod
the corresponding s
SG49A.book Page 13 Friday, September 16, 2005 1:31 PM
s:
nly need to press the correspondingsoft menu key 
nts of a numerical or algebraic variable. For the case 
we can try peeking into the variables z1, R, Q, A12, 
follows: J@@z1@@ @@@R@@ @@@Q@@ @@A12@@ @@»@@ 
en looks like this:
ift key followed by soft menu key labels
ou can display the content of a variable by pressing 
he corresponding soft menu key. Try the following 
@p1@@ ‚ @@z1@@ ‚ @@@R@@ ‚@@@Q@@ ‚ @@A12@@ 
e, you don’t need to press @ (just J and then 
oft menu key.)
This produces the following screen (Algebraic mode in the left, RPN in the 
right)
Notice that this time t
see the remaining var
Listing the content
Use the keystroke com
in the screen. For exa
Press $ to return to
Deleting variab
The simplest way of 
function can be acce
using the FILES menu 
Using function PU
Our variable list con
command PURGE to 
The screen will now s
SG49A.book Page 14 Friday, September 16, 2005 1:31 PM
Page 2-14
 
he contents of program p1 are listed in the screen. To 
iables in this directory, press L.
s of all variables in the screen
bination ‚˜ to list the contents of all variables 
mple:
 normal calculator display.
les
deleting variables is by using function PURGE. This 
ssed directly by using the TOOLS menu (I), or by 
„¡@@OK@@ .
RGE in the stack in Algebraic mode
tains variables p1, z1, Q, R, and α. We will use 
delete variable p1. Press I @PURGE@ J @@p1@@ `. 
how variable p1 removed:
Page 2-15
You can use the PURGE command to erase more than one variable by 
placing their names in a list in the argument of PURGE. For example, if 
now we wanted to purge variables R and Q, simultaneously, we can try 
the following exercise. Press :
I @PURGE@ „ä³J @@@R!@@ ™‚í³J @@@Q!@@
At this point, the screen will show the following command ready to be 
executed:
To finish deleting the
remaining variables:
Using function PU
Assuming that our va
We will use comman
I @PURGE@. The scre
To delete two variabl
a list (in RPN mode,
commas as in Algeb
 J 
Then, press I@PURG
Additional informatio
of the calculator’s use
SG49A.book Page 15 Friday, September 16, 2005 1:31 PM
 variables, press `. The screen will now show the 
RGE in the stack in RPN mode
riable list contains the variables p1, z1, Q, R, and α. 
d PURGE to delete variable p1. Press ³ @@p1@@ ` 
en will now show variable p1 removed:
es simultaneously, say variables R and Q, first create 
 the elements of the list need not be separated by 
raic mode):
„ä³ @@@R!@@ ™³ @@@Q!@@ `
E@ use to purge the variables.
n on variable manipulation is available in Chapter 2 
r’s guide.
UNDO and CMD functions
Functions UNDO and CMD are useful for recovering recent commands, or 
to revert an operation if a mistake was made. These functions are 
associated with the HIST key: UNDO results from the keystroke sequence 
‚¯, while CMD results from the keystroke sequence „®.
CHOOSE boxes vs. Soft MENU
In some of the exercis
of commands display
CHOOSE boxes. He
boxes to Soft MENUs
Although not applied
two options for menus
In this exercise, we u
directory. The steps a
„°˜
@@OK@@ ˜˜˜˜
@@OK@@ ——
SG49A.book Page 16 Friday, September 16, 2005 1:31 PM
Page 2-16
es presented in this chapter we have seen menu lists 
ed in the screen. These menu lists are referred to as 
rein we indicate the way to change from CHOOSE 
, and vice versa, through an exercise.
 to a specific example, the present exercise shows the 
 in the calculator (CHOOSE boxes and soft MENUs). 
se the ORDER command to reorder variables in a 
re shown for Algebraic mode.
Show PROG menu list and select MEMORY
Show the MEMORY menu list and select 
DIRECTORY
Show the DIRECTORY menu list and select ORDER
Page 2-17
There is an alternativ
setting system flag 11
in the calculator’s use
H
The screen shows flag
Press the soft 
will reflect that chang
Press @@OK@@ twice to re
Now, we’ll try to fin
those used above, i.e
menu list, we get sof
menu, i.e.,
@@OK@@
SG49A.book Page 17 Friday, September 16, 2005 1:31 PM
e way to access these menus as soft MENU keys, by 
7. (For information on Flags see Chapters 2 and 24 
r’s guide). To set this flag try the following:
@FLAGS! ———————
 117 not set (CHOOSE boxes), as shown here:
menu key to set flag 117 to soft MENU. The screen 
e:
turn to normal calculator display.
d the ORDER command using similar keystrokes to 
., we start with „°. Notice that instead of a 
t menu labels with the different options in the PROG 
activate the ORDER command
Press B to select the MEMORY soft menu ()@@MEM@@). The display now 
shows:
Press E to select th
The ORDER command
key to find it:
To activate the ORDE
References
For additional informa
display or in the Equ
guide. For CAS (Com
the calculator’s user’s
the calculator’s user’s
NOTE: most of th
current setting of fla
have set the flag bu
you should clear the
SG49A.book Page 18 Friday, September 16, 2005 1:31 PM
Page 2-18
e DIRECTORY soft menu ()@@DIR@@)
 is not shown in this screen. To find it we use the L
R command we press the C(@ORDER) soft menu key.
tion on entering and manipulating expressions in the 
ation Writer see Chapter 2 of the calculator’s user’s 
puter Algebraic System) settings, see Appendix C in 
 guide. For information on Flags see, Chapter 24 in 
 guide.
e examples in this user manual assume that the 
g 117 is its default setting (that is, not set). If you 
t want to strictly follow the examples in this manual, 
 flag before continuing.
Page 3-1
Chapter 3
Calculations with real numbers
This chapter demonstrates the use of the calculator for operations and 
functions related to real numbers. The user should be acquainted with the 
keyboard to identify certain functions available in the keyboard (e.g., SIN, 
COS, TAN, etc.). Also, it is assumed that the reader knows how to change 
the calculator’s oper
boxes (Chapter 1), a
Examples of r
To perform real numb
Real (as opposed to 
most operations. The
mode.
Some operations with
• Use the \ key f
For example, in A
In RPN mode, e.g
• Use the Ykey to
For example, in A
In RPN mode use 
• For addition, subtr
operation key, nam
Examples in ALG 
3
6
4
2
Examples in RPN 
3
6
4
2
Alternatively, in RP
space (#) befor
3
SG49A.book Page 1 Friday, September 16, 2005 1:31 PM
ating system (Chapter 1), use menus and choose 
nd operate with variables (Chapter 2). 
eal number calculations
er calculations it is preferred to have the CAS set to 
Complex) mode. Exact mode is the default mode for 
refore, you may want to start your calculations in this 
 real numbers are illustrated next:
or changing sign of a number. 
LG mode, \2.5`. 
., 2.5\.
 calculate the inverse of a number. 
LG mode, Y2`. 
4Y.
action, multiplication, division, use the proper 
ely, +-*/. 
mode:
.7+5.2`
.3-8.5`
.2*2.5`
.3/4.5`
mode:
.7` 5.2+
.3` 8.5-
.2` 2.5*
.3` 4.5/
N mode, you can separate the operands with a 
e pressing the operator key. Examples:
.7#5.2+
6.3#8.5-
4.2#2.5*
2.3#4.5/
• Parentheses („Ü) can be used to group operations, as well as to 
enclose arguments of functions. 
In ALG mode: 
„Ü5+3.2™/„Ü7-
In RPN mode, you
directly on the stac
5`3
In RPN mode, typi
you to enter the ex
³„
„
For both, ALG and
‚O5+
The expression ca
—
• The absolute value
Example in ALG m
„
Example in RPN m
• The square functio
Example in ALG m
Example in RPN m
The square root fu
calculating in the 
argument, e.g.,
In RPN mode, ente
SG49A.book Page 2 Friday, September 16, 2005 1:31 PM
Page 3-2
2.2`
 do not need the parenthesis, calculation is done 
k:
.2+7`2.2-/
ng the expression between single quotes will allow 
pressionlike in algebraic mode:
Ü5+3.2™/
Ü7-2.2`µ
 RPN modes, using the Equation Writer:
3.2™/7-2.2
n be evaluated within the Equation writer, by using 
———@EVAL@ or, ‚—@EVAL@
 function, ABS, is available through „Ê. 
ode:
Ê\2.32`
ode:
2.32\„Ê
n, SQ, is available through „º. 
ode:
„º\2.3`
ode:
2.3\„º
nction, √, is available through the R key. When 
stack in ALG mode, enter the function before the 
R123.4`
r the number first, then the function, e.g., 
123.4R
Page 3-3
• The power function, ^, is available through the Q key. When 
calculating in the stack in ALG mode, enter the base (y) followed by the 
Q key, and then the exponent (x), e.g.,
5.2Q1.25`
In RPN mode, enter the number first, then the function, e.g.,
5.2`1.25Q
• The root function, XROOT(y,x), is available through the keystroke 
combination ‚»
enter the function 
by commas, e.g.,
‚
In RPN mode, ente
function call, e.g.,
• Logarithms of bas
‚Ã (function
antilogarithm) is c
function is entered
In RPN mode, the
Using powers o
Powers of ten, i.e., n
using the V key. F
\
Or, in RPN mode:
4
• Natural logarithm
the exponential fu
mode, the function
In RPN mode, the
SG49A.book Page 3 Friday, September 16, 2005 1:31 PM
. When calculating in the stack in ALG mode, 
XROOT followed by the arguments (y,x), separated 
»3‚í27`
r the argument y, first, then, x, and finally the 
27`3‚»
e 10 are calculated by the keystroke combination 
 LOG) while its inverse function (ALOG, or 
alculated by using „Â. In ALG mode, the 
 before the argument:
‚Ã2.45`
„Â\2.3`
 argument is entered before the function
2.45‚Ã
2.3\„Â
f 10 in entering data
umbers of the form -4.5 ×10-2, etc., are entered by 
or example, in ALG mode:
4.5V\2`
.5\V2\`
s are calculated by using ‚¹ (function LN) while 
nction (EXP) is calculated by using „¸. In ALG 
 is entered before the argument:
‚¹2.45`
„¸\2.3`
 argument is entered before the function
2.45`‚¹
2.3\`„¸
• Three trigonometric functions are readily available in the keyboard: sine 
(S), cosine (T), and tangent (U). Arguments of these functions 
are angles in either degrees, radians, grades. The following examples 
use angles in degrees (DEG): 
In ALG mode:
In RPN mode:
• The inverse trigono
arcsine („¼)
The answer from t
measure (DEG, RA
In ALG mode:
In RPN mode:
All the functions desc
ALOG, LN, EXP, SIN,
with the fundamental 
expressions. The E
Chapter 2, is ideal
calculator operation m
SG49A.book Page 4 Friday, September 16, 2005 1:31 PM
Page 3-4
S30`
T45`
U135`
30S
45T
135U
metric functions available in the keyboard are the 
, arccosine („¾), and arctangent („À). 
hese functions will be given in the selected angular 
D, GRD). Some examples are shown next: 
„¼0.25`
„¾0.85`
„À1.35`
0.25„¼
0.85„¾
1.35„À
ribed above, namely, ABS, SQ, √, ^, XROOT, LOG, 
 COS, TAN, ASIN, ACOS, ATAN, can be combined 
operations (+-*/) to form more complex 
quation Writer, whose operations is described in 
 for building such expressions, regardless of the 
ode.
Page 3-5
Real number functions in the MTH menu
The MTH („´) menu include a number of mathematical functions 
mostly applicable to real numbers. With the default setting of CHOOSE 
boxes for system flag 117 (see Chapter 2), the MTH menu shows the 
following functions:
The functions are gro
3. lists, 7. probability,
5. real, 6. base, 8. 
constants available in
In general, be aware
for each function, an
first the function and
should enter the argu
Using calculato
1. We will describe i
section with the in
calculator menus. 
different options.
2. To quickly select o
CHOOSE box), si
For example, to se
simply press 4.
Hyperbolic func
Selecting Option 4. H
produces the hyperbo
SG49A.book Page 5 Friday, September 16, 2005 1:31 PM
 
uped by th type of argument (1. vectors, 2. matrices, 
 9. complex) or by the type of function (4. hyperbolic, 
fft). It also contains an entry for the mathematical 
 the calculator, entry 10.
 of the number and order of the arguments required 
d keep in mind that, in ALG mode you should select 
 then enter the argument, while in RPN mode, you 
ment in the stack first, and then select the function. 
r menus
n detail the use of the 4. HYPERBOLIC.. menu in this 
tention of describing the general operation of 
 Pay close attention to the process for selecting 
ne of the numbered options in a menu list (or 
mply press the number for the option in the keyboard. 
lect option 4. HYPERBOLIC.. in the MTH menu, 
tions and their inverses
YPERBOLIC.. , in the MTH menu, and pressing @@OK@@, 
lic function menu:
 
For example, in ALG
tanh(2.5), is the follow
„´
In the RPN mode, 
following:
2.
The operations shown
for system flag 117 (
this flag (see Chapte
follows (left-hand side
Pressing L shows t
Thus, to select, for ex
format press )@@HYP@ , to
SG49A.book Page 6 Friday, September 16, 2005 1:31 PM
Page 3-6
 mode, the keystroke sequence to calculate, say, 
ing:
4@@OK@@ 5@@OK@@ 2.5`
the keystrokes to perform this calculation are the 
5`„´4@@OK@@ 5@@OK@@ 
 above assume that you are using the default setting 
CHOOSE boxes). If you have changed the setting of 
r 2) to SOFT menu, the MTH menu will show as 
 in ALG mode, right – hand side in RPN mode):
 
he remaining options:
 
ample, the hyperbolic functions menu, with this menu 
 produce: 
 
Page 3-7
Finally, in order to select, for example, the hyperbolic tangent (tanh) 
function, simply press @@TANH@.
For example, to calculate tanh(2.5), in the ALG mode, when using SOFT 
menus over CHOOSE boxes, follow this procedure:
„
In RPN mode, the sam
2
As an exercise of ap
values:
Operations w
Numbers in the calcu
possible to calculate
produce a result with
The UNITS men
The units menu 
‚Û(associated 
CHOOSE boxes, the 
NOTE: To see additional options in these soft menus, press the L
key or the „«keystroke sequence.
SINH (2.5) =
COSH (2.5)
TANH(2.5) =
EXPM(2.0) =
SG49A.book Page 7 Friday, September 16, 2005 1:31 PM
´@@HYP@ @@TANH@ 2.5`
e value is calculated using:
.5`„´ )@@HYP@ @@TANH@
plications of hyperbolic functions, verify the following 
ith units
lator can have units associated with them. Thus, it is 
 results involving a consistent system of units and 
 the appropriate combination of units.
u
is launched by the keystroke combination 
with the 6 key). With system flag 117 set to 
result is the following menu:
 
 6.05020.. ASINH(2.0) = 1.4436…
 = 6.13228.. ACOSH (2.0) = 1.3169…
 0.98661.. ATANH(0.2) = 0.2027…
 6.38905…. LNP1(1.0) = 0.69314….
Option 1. Tools.. con
later). Options 2. Le
number of units for
selecting option 8. Fo
The user will recogniz
very often nowadays)
dynes, gf = grams – f
a unit of mass), kip =
distinguish from poun
To attach a unit obje
underscore. Thus, a f
For extensive operatio
way of attaching un
Chapter 2), and us
following menus. Pre
SG49A.book Page 8 Friday, September 16, 2005 1:31 PM
Page 3-8
tains functions used to operate on units (discussed 
ngth.. through 17.Viscosity.. contain menus with a 
 each of the quantities described. For example, 
rce.. shows the following units menu:
 
e most of these units (some, e.g., dyne, are not used 
 from his or her physics classes: N = newtons, dyn = 
orce (to distinguish from gram-mass, or plainly gram, 
 kilo-poundal (1000 pounds), lbf = pound-force (to 
d-mass), pdl = poundal.
ct to a number, the number must be followed by an 
orce of 5 N will be entered as 5_N.
ns with units SOFT menus provide a more convenient 
its. Change system flag 117 to SOFT menus (see 
e the keystroke combination ‚Û to get the 
ss Lto move to the next menu page.
 
Page 3-9
Pressing on the appropriate soft menu key will open the sub-menu of units 
for that particular selection. For example, for the @)SPEED sub-menu, the 
following units are available:
Pressing the soft menu
Recall that you can a
‚˜, e.g., for the
Available units
For a complete list o
user’s guide.
Attaching units
To attach a unit obje
underscore (‚Ý
5_N. 
Here is the sequence
flag 117 set to CHOO
5
To enter this same q
following keystrokes:
NOTE: Use the 
navigate through th
NOTE: If you forge
where N here repre
SG49A.book Page 9 Friday, September 16, 2005 1:31 PM
 
 key @)UNITS will take you back to the UNITS menu.
lways list the full menu labels in the screen by using 
 @)ENRG set of units the following labels will be listed:
 
f available units see Chapter 3 in the calculator’s 
 to numbers
ct to a number, the number must be followed by an 
, key(8,5)). Thus, a force of 5 N will be entered as 
 of steps to enter this number in ALG mode, system 
SE boxes:
‚Ý‚Û8@@OK@@ @@OK@@ `
uantity, with the calculator in RPN mode, use the 
L key or the „«keystroke sequence to 
e menus.
t the underscore, the result is the expression 5*N, 
sents a possible variable name and not Newtons.
5‚Û8@@OK@@ @@OK@@
Notice that the underscore is entered automatically when the RPN mode is 
active.
The keystroke sequences to enter units when the SOFT menu option is 
selected, in both ALG and RPN modes, are illustrated next. For example, 
in ALG mode, to enter the quantity 5_N use:
5‚Ý‚ÛL @)@FORCE @@@N@@ `
The same quantity, en
Unit prefixes
You can enter prefixe
from the SI system. T
name, and by the e
prefix:
(*) In the SI system, t
calculator, however.
To enter these prefixe
example, to enter 123
NOTE: You can en
units with the ~k
entry: 5_N
Prefix Name
Y yotta
Z zetta
E exa
P peta
T tera
G giga
M mega
k,K kilo
h,H hecto
D(*) deka
SG49A.book Page 10 Friday, September 16, 2005 1:31 PM
Page 3-10
tered in RPN mode uses the following keystrokes:
5‚ÛL @)@FORCE @@@N@@
s for units according to the following table of prefixes 
he prefix abbreviation is shown first, followed by its 
xponent x in the factor 10x corresponding to each 
his prefix is da rather than D. Use D for deka in the 
s, simply type the prefix using the ~ keyboard. For 
 pm (picometer), use:
ter a quantity with units by typing the underline and 
eyboard, e.g., 5‚Ý~n will produce the 
x Prefix Name x
+24 d deci -1
+21 c centi -2
+18 m milli -3
+15 µ micro -6
+12 n nano -9
+9 p pico -12
+6 f femto -15
+3 a atto -18
+2 z zepto -21
+1 y yocto -24
Page 3-11
123‚Ý~„p~„m
Using UBASE (type the name) to convert to the default unit (1 m) results in:
 
Operations with
Here are some calcu
warned that, when m
enclosed each quanti
for example, the 
(12.5_m)*(5.2_yd) `
which shows as 65_
function UBASE (find 
To calculate a divisio
which transformed to 
NOTE: Recall tha
keystroke combinati
SG49A.book Page 11 Friday, September 16, 2005 1:31 PM
 units
lation examples using the ALG operating mode. Be 
ultiplying or dividing quantities with units, you must 
ty with its units between parentheses. Thus, to enter, 
product 12.5m × 5.2 yd, type it to read 
:
(m⋅yd). To convert to units of the SI system, use 
it using the command catalog, ‚N): 
n, say, 3250 mi / 50 h, enter it as 
(3250_mi)/(50_h) `
SI units, with function UBASE, produces:
t the ANS(1) variable is available through the 
on „î(associated with the ` key).
Addition and subtraction can be performed, in ALG mode, without using 
parentheses, e.g., 5 m + 3200 mm, can be entered simply as 
5_m + 3200_mm `.
More complicated expression require the use of parentheses, e.g., 
(12_mm)*(1_cm^2)/(2_s) `:
Stack calculations in the RPN mode do not require you to enclose the 
different terms in pare
3
These operations prod
Unit conversion
The UNITS menu c
following functions:
Examples of function 
UNIT/TOOLS function
guide.
For example, to conve
CONVERT(x,y) conv
UBASE(x) conv
UVAL(x) extra
UFACT(x,y) facto
�UNIT(x,y) comb
SG49A.book Page 12 Friday, September 16, 2005 1:31 PM
Page 3-12
ntheses, e.g., 
12 @@@m@@@ `1.5 @@yd@@ `*
250 @@mi@@ `50 @@@h@@@ `/
uce the following output:
s
ontains a TOOLS sub-menu, which provides the 
CONVERT are shown below. Examples of the other 
s are available in Chapter 3 of the calculator’s user’s 
rt 33 watts to btu’s use either of the following entries:
CONVERT(33_W,1_hp) `
CONVERT(33_W,11_hp) `
ert unit object x to units of object y
ert unit object x to SI units
ct the value from unit object x
rs a unit y from unit object x
ines value of x with units of y
Page 3-13
Physical constants in the calculator
The calculator’s physical constants are contained in a constants library
activated with the command CONLIB. To launch this command you could 
simply type it in the stack: ~~conlib`, or, you can select 
the command CONLIB from the command catalog, as follows: First, 
launch the catalog by using: ‚N~c. Next, use the up and down 
arrow keys —˜ to select CONLIB. Finally, press @@OK@@. Press `, if 
needed. Use the up 
the list of constants in
The soft menu keys 
include the following 
(*) Activated only if th
This is the way the to
option VALUE is selec
To see the values of t
the @ENGL option:
SI when
ENGL when
(*)
UNIT when
VALUE when
�STK copie
QUIT exit co
SG49A.book Page 13 Friday, September 16, 2005 1:31 PM
and down arrow keys (—˜) to navigate through 
 your calculator.
corresponding to this CONSTANTS LIBRARY screen 
functions:
e VALUE option is selected.
p of the CONSTANTS LIBRARY screen looks when the 
ted (units in the SI system):
he constants in the English (or Imperial) system, press 
 selected, constants values are shown in SI units (*)
 selected, constants values are shown in English units 
 selected, constants are shown with units attached (*)
 selected, constants are shown without units
s value (with or without units) to the stack
nstants library
If we de-select the UN
(English units selected
To copy the value of 
@²STK, then, press @QUI
look like this:
The display shows w
here, Vm, is the tag
number will ignore th
which produces:
The same operation 
(after the value of Vm
SG49A.book Page 14 Friday, September 16, 2005 1:31 PM
Page 3-14
ITS option (press @UNITS ) only the values are shown 
 in this case):
Vm to the stack, select the variable name, and press 
T@. For the calculator set to the ALG, the screen will 
hat is called a tagged value, Vm:359.0394. In 
 of this result. Any arithmetic operation with this 
e tag. Try, for example:
‚¹2*„î`
in RPN mode will require the following keystrokes 
 was extracted from the constants library):
2`*‚¹
Page 3-15
Defining and using functions
Users can define their own functions by using the DEFINE command
available thought the keystroke sequence „à (associated with the
2 key). The function must be entered in the following format:
Function_name(arguments) = expression_containing_arguments
For example, we could define a simple function 
Suppose that you ha
discrete values and, t
and get the result yo
right-hand side for e
assume you have set
sequence of keystroke
„à³
‚¹~„
The screen will look li
Press the J key, an
soft menu key (@@@H@@). 
The screen will show 
Thus, the variable H c
This is a simple pro
calculator. This prog
20 and 21 in the cal
Ch03_RealNumbersQS.fm Page 15 Friday, February 24, 2006 6:19 PM
H(x) = ln(x+1) + exp(-x)
ve a need to evaluate this function for a number of
herefore, you want to be able to press a single button
u want without having to type the expression in the
achseparate value. In the following example, we
 your calculator to ALG mode. Enter the following
s:
~h„Ü~„x™‚Å
x+1™+„¸~„x`
ke this:
d you will notice that there is a new variable in your
 To see the contents of this variable press ‚@@@H@@.
now:
ontains a program defined by:
<< � x ‘LN(x+1) + EXP(x)’ >>
gram in the default programming language of the
ramming language is called UserRPL (See Chapters
culator’s user’s guide). The program shown above is
relatively simple and consists of two parts, contained between the program
containers 
This is to be interpreted as saying: enter a value that is temporarily
assigned to the name x (referred to as a local variable), evaluate the
expression between q
evaluated expression.
To activate the funct
followed by the 
„Ü2`. S
In the RPN mode, to
press the soft menu 
example, you could t
be entered by using: 
Reference
Additional informatio
is contained in Chapt
• Input: � x � x
• Process: ‘LN(x+1) + EXP(x) ‘
Ch03_RealNumbersQS.fm Page 16 Friday, February 24, 2006 6:19 PM
Page 3-16
uotes that contain that local variable, and show the
ion in ALG mode, type the name of the function
argument between parentheses, e.g., @@@H@@@
ome examples are shown below:
 
 activate the function enter the argument first, then
key corresponding to the variable name @@@H@@@ . For
ry: 2@@@H@@@ . The other examples shown above can
1.2@@@H@@@ , 2`3/@@@H@@@.
n on operations with real numbers with the calculator
er 3 of the user’s guide.
Page 4-1
Chapter 4
Calculations with complex numbers
This chapter shows examples of calculations and application of functions to 
complex numbers.
Definitions
A complex number z
numbers, and i is th
number x + iy has a r
The complex number 
the x–y plane, with t
referred to as the ima
A complex number 
representation. An al
A complex number c
representation) as z =
is the magnitude of th
the argument of the c
The relationship be
complex numbers is 
complex conjugate o
= re –iθ . The comple
z about the real (x) a
can be thought of as 
Setting the ca
To work with complex
The COMPLEX mode 
option _Complex che
SG49A.book Page 1 Friday, September 16, 2005 1:31 PM
 is a number z = x + iy, where x and y are real 
e imaginary unit defined by i² = –1. The complex 
eal part, x = Re(z), and an imaginary part, y = Im(z). 
z = zx + iy is often used to represent a point P(x,y) in 
he x-axis referred to as the real axis, and the y-axis 
ginary axis. 
in the form x + iy is said to be in a rectangular
ternative representation is the ordered pair z = (x,y). 
an also be represented in polar coordinates (polar
 reiθ = r·cosθ + i r·sinθ, where r = |z| = 
e complex number z, and θ = Arg(z) = arctan(y/x) is 
omplex number z. 
tween the Cartesian and polar representation of 
given by the Euler formula: ei iθ = cosθ + i sinθ. The 
f a complex number (z = x + iy = re iθ) is = x – iy
x conjugate of i can be thought of as the reflection of 
xis. Similarly, the negative of z, –z = –x –iy = –re iθ, 
the reflection of z about the origin.
lculator to COMPLEX mode
 numbers select the CAS complex mode:
H )@@CAS@ ˜˜™ 
will be selected if the CAS MODES screen shows the 
cked, i.e., 
22
yx +
z
Press @@OK@@ , twice, to r
Entering comple
Complex numbers in
Cartesian representa
calculator will be s
example, with the cal
(3.5, -1.2), is entered
„Ü3
A complex number c
ALG mode, 3.5-1.2i i
3.
In RPN mode, thes
keystrokes:
„Ü3
(Notice that the chan
been entered, in the o
NOTE: to enter the
key.
SG49A.book Page 2 Friday, September 16, 2005 1:31 PM
Page 4-2
eturn to the stack.
x numbers
 the calculator can be entered in either of the two 
tions, namely, x+iy, or (x,y). The results in the 
hown in the ordered-pair format, i.e., (x,y). For 
culator in ALG mode, the complex number 
 as:
.5‚í\1.2`
an also be entered in the form x+iy. For example, in 
s entered as (accept mode changes):
5 -1.2*„¥`
e numbers could be entered using the following 
.5‚í1.2\`
ge-sign keystroke is entered after the number 1.2 has 
pposite order as the ALG mode exercise).
 unit imaginary number alone type „¥, the I 
Page 4-3
Polar representation of a complex number
The polar representation of the complex number 3.5-1.2i, entered above, 
is obtained by changing the coordinate system to cylindrical or polar 
(using function CYLIN). You can find this function in the catalog 
(‚N). You can also change the coordinate to polar using H. 
Changing to polar coordinate with standard notation and the angular 
measure in radians, produces the result in RPN mode:
The result shown ab
0.33029…. The ang
Return to Cartesian 
(available in the ca
representation is writ
into the calculator by
symbol (∠) can be e
number z = 5.2e1.5i,
stack, before and afte
Because the coordin
calculator automatic
coordinates, i.e., x 
(0.3678…, 5.18…).
On the other hand, if
(use CYLIN), entering
numbers, will produc
coordinates, enter th
stack, before and afte
SG49A.book Page 3 Friday, September 16, 2005 1:31 PM
ove represents a magnitude, 3.7, and an angle 
le symbol (∠) is shown in front of the angle measure.
or rectangular coordinates by using function RECT 
talog, ‚N). A complex number in polar 
ten as z = r⋅eiθ. You can enter this complex number 
 using an ordered pair of the form (r, ∠θ). The angle 
ntered as ~‚6. For example, the complex 
 can be entered as follows (the figures show the RPN 
r entering the number):
 
ate system is set to rectangular (or Cartesian), the 
ally converts the number entered to Cartesian 
= r cos θ, y = r sin θ, resulting, for this case, in 
 the coordinate system is set to cylindrical coordinates 
 a complex number (x,y), where x and y are real 
e a polar representation. For example, in cylindrical 
e number (3.,2.). The figure below shows the RPN 
r entering this number:
 
Simple operations with complex numbers
Complex numbers ca
(+-*/). 
that i2= -1. Operati
real numbers. For ex
set to Complex, try th
The CMPLX m
There are two CM
calculator. One is 
Chapter 3) and one d
menus are presented 
CMPLX menu th
Assuming that system
the CMPLX sub-men
„´9@@OK@@ . T
SG49A.book Page 4 Friday, September 16, 2005 1:31 PM
Page 4-4
n be combined using the four fundamental operations 
The results follow the rules of algebra with the caveat 
ons with complex numbers are similar to those with 
ample, with the calculator in ALG mode and the CAS 
e following operations:
(3+5i) + (6-3i) = (9,2);
(5-2i) - (3+4i) = (2,-6)
(3-i)·(2-4i) = (2,-14);
(5-2i)/(3+4i) = (0.28,-1.04)
1/(3+4i) = (0.12, -0.16) ;
-(5-3i) = -5 + 3i
enus
PLX (CoMPLeX numbers) menus available in the 
available through the MTH menu (introduced in 
irectly into the keyboard (‚ß). The two CMPLX 
next.
rough the MTH menu
 flag 117 is set to CHOOSE boxes (see Chapter 2), 
u within the MTH menu is accessed by using: 
he functions available are the following:
 
Page 4-5
The first menu (options 1 through 6) shows the following functions:
Examples of applications of these functions are shown next in RECT 
coordinates. Recall 
argument, while in RP
the function. Also, r
labels by changing th
RE(z) Real part of a complex number
IM(z) Imaginary part of a complex number
C→R(z) Separates a complex number into its real and imaginary 
parts
R→C(x,y) Form
y
ABS(z) Calc
ARG(z) Calc
SIGN(z) Calc
|z|.
NEG(z) Chan
CONJ(z) Prod
SG49A.book Page 5 Friday, September 16, 2005 1:31 PM
that, for ALG mode, the function must precede the 
N mode, you enter the argument first, and then select 
ecall that you can get these functions as soft menu 
e setting of system flag 117 (See Chapter 2).
 
s the complexnumber (x,y) out of real numbers x and 
ulates the magnitude of a complex number.
ulates the argument of a complex number.
ulates a complex number of unit magnitude as z/
ges the sign of z
uces the complex conjugate of z
CMPLX menu in keyboard
A second CMPLX menu is accessible by using the right-shift option 
associated with the 1 key, i.e., ‚ß. With system flag 117 set to 
CHOOSE boxes, the keyboard CMPLX menu shows up as the following 
screens:
The resulting menu in
previous section, nam
also includes function
combination „¥
Functions app
Many of the keyboard
Chapter 3 for real n
complex numbers. T
the following example
SG49A.book Page 6 Friday, September 16, 2005 1:31 PM
Page 4-6
 
clude some of the functions already introduced in the 
ely, ARG, ABS, CONJ, IM, NEG, RE, and SIGN. It 
 i which serves the same purpose as the keystroke 
.
lied to complex numbers
-based functions and MTH menu functions defined in 
umbers (e.g., SQ, LN, ex, etc.), can be applied to 
he result is another complex number, as illustrated in 
s.
 
 
Page 4-7
 
Function DRO
Function DROITE take
and x2+iy2, and retu
that contains the po
between points A(5, 
Algebraic mode):
Function DROITE is 
calculator is in APPRO
Reference
Additional informatio
Chapter 4 of the calc
NOTE: When usin
complex numbers t
angular measure s
calculation of these
SG49A.book Page 7 Friday, September 16, 2005 1:31 PM
ITE: equation of a straight line
s as argument two complex numbers, say, x1 + iy1
rns the equation of the straight line, say, y = a + bx, 
ints (x1, y1) and (x2, y2). For example, the line 
-3) and B(6, 2) can be found as follows (example in 
found in the command catalog (‚N). If the 
X mode, the result will be Y = 5.*(X-5.)-3.
n on complex number operations is presented in 
ulator’s user’s guide.
g trigonometric functions and their inverses with 
he arguments are no longer angles. Therefore, the 
elected for the calculator has no bearing in the 
 functions with complex arguments.
SG49A.book Page 8 Friday, September 16, 2005 1:31 PM
Page 5-1
Chapter 5
Algebraic and arithmetic operations
An algebraic object, or simply, algebraic, is any number, variable name or 
algebraic expression that can be operated upon, manipulated, and 
combined according to the rules of algebra. Examples of algebraic objects 
are the following:
Entering alge
Algebraic objects ca
quotes directly into s
For example, to ente
level 1 use:
³„
An algebraic object c
to the stack, or opera
of the Equation Write
the following algebra
After building the ob
modes shown below)
• A number: 1
• A variable name: ‘a
• An expression: ‘p
• An equation: ‘p
SG49A.book Page 1 Friday, September 16, 2005 1:31 PM
braic objects
n be created by typing the object between single 
tack level 1 or by using the equation writer (EQW). 
r the algebraic object ‘π*D^2/4’ directly into stack 
ì*~dQ2/4`
an also be built in the Equation Writer and then sent 
ted upon in the Equation Writer itself. The operation 
r was described in Chapter 2. As an exercise, build 
ic object in the Equation Writer:
ject, press ` to show it in the stack (ALG and RPN 
:
 
2.3, 15.2_m, ‘π’, ‘e’, ‘i’
’, ‘ux’, ‘width’, etc.
*D^2/4’, ’f*(L/D)*(V^2/(2*g))’,
*V = n*R*T’, ‘Q=(Cu/n)*A(y)*R(y)^(2/3)*√So’
Simple operations with algebraic objects
Algebraic objects can be added, subtracted, multiplied, divided (except by 
zero), raised to a power, used as arguments for a variety of standard 
functions (exponential, logarithmic, trigonometry, hyperbolic, etc.), as you 
would any real or complex number. To demonstrate basic operations with 
algebraic objects, let’s create a couple of objects, say ‘π*R^2’ and 
‘g*t^2/4’, and store them in variables A1 and A2 (See Chapter 2 to learn 
how to create variabl
for storing variables A
³„ì
resulting in:
The keystrokes corresp
„ì
After storing the varia
variables as follows:
In ALG mode, the fo
with the algebraics c
recover variable men
@@A1@@ + @
SG49A.book Page 2 Friday, September 16, 2005 1:31 PM
Page 5-2
es and store values in them). Here are the keystrokes 
1 in ALG mode:
*~rQ2™K~a1`
onding to RPN mode are:
~r`2Q*~a1K
ble A2 and pressing the key, the screen will show the 
llowing keystrokes will show a number of operations 
ontained in variables @@A1@@ and @@A2@@ (press J to 
u):
@A2@@ ` @@A1@@ - @@A2@@ `
 
Page 5-3
@@A1@@ *@@A2@@ ` @@A1@@ / @@A2@@ `
 
‚¹
The same results ar
keystrokes:
Functions in the
The ALG (Algebraic)
‚× (associated
CHOOSE boxes, the 
Rather than listing the
is invited to look up
IL@)HELP@`. 
the function. For exa
the up and down arr
window.
@@A1@@ @
@@A1@@ @
@@A1@@ ‚
SG49A.book Page 3 Friday, September 16, 2005 1:31 PM
@@A1@@ „¸@@A2@@
 
e obtained in RPN mode if using the following 
 ALG menu 
 menu is available by using the keystroke sequence 
 with the 4 key). With system flag 117 set to 
ALG menu shows the following functions:
 
 description of each function in this manual, the user 
 the description using the calculator’s help facility: 
To locate a particular function, type the first letter of 
mple, for function COLLECT, we type ~c, then use 
ow keys, —˜, to locate COLLECT within the help 
@A2@@ +µ @@A1@@ @@A2@@ -µ
@A2@@ *µ @@A1@@ @@A2@@ /µ
 ¹µ @@A2@@ „ ¸µ
To complete the operation press @@OK@@. Here is the help screen for function 
COLLECT:
We notice that, at the
suggests links to oth
FACTOR. To move d
for EXPAND, and @SE
the following informa
FACTOR:
Copy the examples 
example, for the EXP
key to get the followin
the command):
Thus, we leave for th
the ALG menu. This i
SG49A.book Page 4 Friday, September 16, 2005 1:31 PM
Page 5-4
 
 bottom of the screen, the line See: EXPAND FACTOR 
er help facility entries, the functions EXPAND and 
irectly to those entries, press the soft menu key @SEE1!
E2! for FACTOR. Pressing @SEE1!, for example, shows 
tion for EXPAND, while @SEE2! shows information for 
 
provided onto your stack by pressing @ECHO!. For 
AND entry shown above, press the @ECHO! soft menu 
g example copied to the stack (press ` to execute 
 
e user to explore the applications of the functions in 
s a list of the commands:
Page 5-5
 
For example, for func
entry:
Operations w
The calculator offers 
expressions containin
as well as trigonomet
Expansion and
The „Ð produc
NOTE: Recall that
mode, you must en
example, the examp
³
At this point, select 
the catalog ‚N
SG49A.book Page 5 Friday, September 16, 2005 1:31 PM
tion SUBST, we find the following CAS help facility 
 
ith transcendental functions
a number of functions that can be used to replace 
g logarithmic and exponential functions („Ð), 
ric functions (‚Ñ).
 factoring using log-exp functions
es the following menu:
 
, to use these, or any other functions in the RPN 
ter the argument first, and then the function. For 
le for TEXPAND, in RPN mode will be set up as:
„¸+~x+~y`
function TEXPAND from menu ALG (or directly from 
), to complete the operation.
Information and examples on these commands are available in the help 
facility of the calculator. For example, the description of EXPLN is shown in 
the left-hand side, and the example from the help facility is shown to the 
right:
Expansion and 
functions
The TRIG menu, tri
functions:
These functions allow
of trigonometric func
ACOS2S allows to 
expression in terms o
Description of these 
available in the cal
invited to explore this
TRIG menu.
SG49A.book Page 6 Friday, September 16, 2005 1:31 PM
Page 5-6
 
factoringusing trigonometric 
ggered by using ‚Ñ, shows the following 
 
 to simplify expressions by replacing some category 
tions for another one. For example, the function 
replace the function arccosine (acos(x)) with its 
f arcsine (asin(x)).
commands and examples of their applications are 
culator’s help facility (IL@HELP). The user is 
 facility to find information on the commands in the 
Page 5-7
Functions in the ARITHMETIC menu
The ARITHMETIC menu is triggered through the keystroke combination 
„Þ (associated with the 1 key). With system flag 117 set to 
CHOOSE boxes, „Þ shows the following menu:
Out of this menu l
PROPFRAC, SIMP2
integer numbers o
1. INTEGER, 2. PO
are actually sub-m
objects. When sy
menu („Þ) p
Following, we pre
and SIMP2 in the 
The functions assoc
POLYNOMIAL, MOD
Chapter 5 in the cal
some applications to 
FACTORS:
 
ist, options 5 through 9 (DIVIS, FACTORS, LGCD, 
) correspond to common functions that apply to 
r to polynomials. The remaining options ( 
LYNOMIAL, 3. MODULO, and 4. PERMUTATION) 
enus of functions that apply to specific mathematical 
stem flag 117 is set to SOFT menus, the ARITHMETIC 
roduces:
 
sent the help facility entries for functions FACTORS 
ARITHMETIC menu(IL@HELP):
iated with the ARITHMETIC submenus: INTEGER, 
ULO, and PERMUTATION, are presented in detail in 
culator’s user’s guide. The following sections show 
polynomials and fractions.
SIMP2:
Polynomials
Polynomials are algebraic expressions consisting of one or more terms 
containing decreasing powers of a given variable. For example, 
‘X^3+2*X^2-3*X+2’ is a third-order polynomial in X, while ‘SIN(X)^2-2’ is 
a second-order polynomial in SIN(X). Functions COLLECT and EXPAND, 
shown earlier, can be used on polynomials. Other applications of 
polynomial functions are presented next:
The HORNER fu
The function HORNE
Horner division, or sy
a), i.e., HORNER(P(X
For example, 
HORNER(‘X^3
i.e., X3+2X2-3X+1 = 
{X^5-5*X^4+2
i.e., X6-1 = (X5-5*X4+
The variable VX
Most polynomial exa
because a variable c
directory that takes, 
preferred independen
Avoid using the varia
get it confused with t
variable see Appendi
The PCOEF func
Given an array conta
generates an array 
polynomial. The c
independent variable
PCOEF([-2, 
which represents the 
SG49A.book Page 8 Friday, September 16, 2005 1:31 PM
Page 5-8
nction
R („Þ, POLYNOMIAL, HORNER) produces the 
nthetic division, of a polynomial P(X) by the factor (X-
),a) = {Q(X), a, P(a)}, where P(X) = Q(X)(X-a)+P(a). 
+2*X^2-3*X+1’,2) = {X^2+4*X+5 2 11}
(X2+4X+5)(X-2)+11. Also,
HORNER(‘X^6-1’,-5)=
5*X^3-125*X^2+625*X-3125 -5 15624}
25X3-125X2+625X-3125)(X+5)+15624.
mples above were written using variable X. This is 
alled VX exists in the calculator’s {HOME CASDIR} 
by default, the value of ‘X’. This is the name of the 
t variable for algebraic and calculus applications. 
ble VX in your programs or equations, so as to not 
he CAS’ VX. For additional information on the CAS 
x C in the calculator’s user’s guide.
tion
ining the roots of a polynomial, the function PCOEF 
containing the coefficients of the corresponding 
oefficients correspond to decreasing order of the 
. For example:
–1, 0 ,1, 1, 2]) = [1. –1. –5. 5. 4. –4. 0.],
polynomial X6-X5-5X4+5X3+4X2-4X.
Page 5-9
The PROOT function
Given an array containing the coefficients of a polynomial, in decreasing 
order, the function PROOT provides the roots of the polynomial. Example, 
from X2+5X+6 =0, PROOT([1, –5, 6]) = [2. 3.].
The QUOT and REMAINDER functions
The functions QUOT 
Q(X) and the remai
P1(X) and P2(X). In o
from P1(X)/P2(X) = Q
QU
REM
Thus, we can write: (X
The PEVAL func
The function PEVAL (
polynomial 
p(x) = 
given an array of co
The result is the eval
ARITHMETIC menu, in
PEVAL([1,5,6,1],5) =
Additional applicatio
in the calculator’s use
Fractions
Fractions can be exp
FACTOR, from the AL
EXPAND(‘(1+X)^3/((
EXPAND(‘(X^2)*(X+Y
FACTOR(‘(3*X^3-2*X
NOTE: you could g
PARTFRAC(‘
SG49A.book Page 9 Friday, September 16, 2005 1:31 PM
and REMAINDER provide, respectively, the quotient 
nder R(X), resulting from dividing two polynomials, 
ther words, they provide the values of Q(X) and R(X) 
(X) + R(X)/P2(X). For example,
OT(‘X^3-2*X+2’, ‘X-1’) = ‘X^2+X-1’
AINDER(‘X^3-2*X+2’, ‘X-1’) = 1.
3-2X+2)/(X-1) = X2+X-1 + 1/(X-1).
tion 
Polynomial EVALuation) can be used to evaluate a 
an⋅x
n+an-1⋅x 
n-1+ …+ a2⋅x
2+a1⋅x+ a0,
efficients [an, an-1, … a2, a1, a0] and a value of x0. 
uation p(x0). Function PEVAL is not available in the 
stead use the CALC/DERIV&INTEG Menu. Example: 
 281.
ns of polynomial functions are presented in Chapter 5 
r’s guide.
anded and factored by using functions EXPAND and 
G menu (‚×). For example:
X-1)*(X+3))’)=‘(X^3+3*X^2+3*X+1)/(X^2+2*X-3)’
)/(2*X-X^2)^2)’)=‘(X+Y)/(X^2-4*X+4)’
^2)/(X^2-5*X+6)’)=‘X^2*(3*X-2)/((X-2)*(X-3))’
et the latter result by using PARTFRAC:
(X^3-2*X+2)/(X-1)’) = ‘X^2+X-1 + 1/(X-1)’.
FACTOR(‘(X^3-9*X)/(X^2-5*X+6)’ )=‘X*(X+3)/(X-2)’
The SIMP2 function
Function SIMP2, in the ARITHMETIC menu, takes as arguments two 
numbers or polynomials, representing the numerator and denominator of a 
rational fraction, and returns the simplified numerator and denominator. 
For example:
SIMP2(‘X
The PROPFRAC
The function PROPF
fraction, i.e., an in
decomposition is pos
PROP
The PARTFRAC 
The function PARTFR
fractions that produce
PARTFRAC(‘(2*X^6-1
7*X^4+11*X^3-7*X
‘2*X+(1/2/(X-2)+5/
The FCOEF func
The function FCOEF,
menu, is used to obta
fraction.
The input for the fun
multiplicity (i.e., how 
followed by their m
example, if we want 
0 with multiplicity 3, a
2 and –3 with multip
NOTE: If a rationa
the fraction result fr
result from solving t
SG49A.book Page 10 Friday, September 16, 2005 1:31 PM
Page 5-10
^3-1’,’X^2-4*X+3’) = {‘X^2+X+1’,‘X-3’}
 function
RAC converts a rational fraction into a “proper” 
teger part added to a fractional part, if such 
sible. For example:
PROPFRAC(‘5/4’) = ‘1+1/4’
FRAC(‘(x^2+1)/x^2’) = ‘1+1/x^2’
function
AC decomposes a rational fraction into the partial 
 the original fraction. For example:
4*X^5+29*X^4-37*X^3+41*X^2-16*X+5)/(X^5-
^2+10*X)’) = 
(X-5)+1/2/X+X/(X^2+1))’
tion
 available through the ARITHMETIC/POLYNOMIAL 
in a rational fraction, given the roots and poles of the 
ction is a vector listing the roots followed by their 
many times a given root is repeated), and the poles 
ultiplicity represented as a negative number. For 
to create a fraction having roots 2 with multiplicity 1, 
nd -5 with multiplicity 2, and poles 1 with multiplicity 
licity 5, use:
l fraction is given as F(X) = N(X)/D(X), the roots of 
om solving the equation N(X) = 0, while the poles 
he equation D(X) = 0.
Page 5-11
FCOEF([2,1,0,3,–5,2,1,–2,–3,–5])=‘(X--5)^2*X^3*(X-2)/(X-+3)^5*(X-1)^2’
If you press µ„î` (or, simply µ, in RPN mode) you will get:
‘(X^6+8*X^5+5*X^4-50*X^3)/(X^7+13*X^6+61*X^5+105*X^4-
45*X^3-297*X62-81*X+243)’
The FROOTS function
The function FROOTS
the roots and poles 
FROOTS to the result 
1. –5 2.]. The res
negative number, an
number. In this ca
respectively, and the
respectively.
Another example is: 
1. 2 1.], i.e., poles =
Complex mode selec
[0 –2. 1 –1. – (
Step-by-step 
fractions
By setting the CAS
simplifications of frac
fashion. This is very
example of dividing 
is shown in detail in
following example sh
the ARITH/POLYNOM
SG49A.book Page 11 Friday, September 16, 2005 1:31 PM
, in the ARITHMETIC/POLYNOMIAL menu, obtains 
of a fraction. As an example, applying function 
produced above, will result in: [1 –2. –3 –5. 0 3. 2 
ult shows poles followed by their multiplicity as a 
d rootsfollowed by their multiplicity as a positive 
se, the poles are (1, -3) with multiplicities (2,5) 
 roots are (0, 2, -5) with multiplicities (3, 1, 2), 
FROOTS(‘(X^2-5*X+6)/(X^5-X^2)’) = [0 –2. 1 –1. 3 
 0 (2), 1(1), and roots = 3(1), 2(1). If you have had 
ted, then the results would be: 
(1+i*√3)/2) –1. – ((1–i*√3)/2) –1. 3 1. 2 1.].
operations with polynomials and 
 modes to Step/step the calculator will show 
tions or operations with polynomials in a step-by-step 
 useful to see the steps of a synthetic division. The 
 Appendix C of the calculator’s user’s guide. The 
ows a lengthier synthetic division (DIV2 is available in 
IAL menu):
2
235
23
−
−+−
X
XXX
1
1
2
9
−
−
X
X
 
Reference
Additional informati
arithmetic operations
guide.
SG49A.book Page 12 Friday, September 16, 2005 1:31 PM
Page 5-12
 
 
 
 
on, definitions, and examples of algebraic and 
 are presented in Chapter 5 of the calculator’s user’s 
Page 6-1
Chapter 6
Solution to equations
Associated with the 7 key there are two menus of equation-solving 
functions, the Symbolic SOLVer („Î), and the NUMerical SoLVer 
(‚Ï). Following, we present some of the functions contained in 
these menus. 
Symbolic solu
Here we describe so
Activate the menu b
system flag 117 set 
available: 
Functions ISOL and 
polynomial equation
where the unknown 
Finally, function ZERO
Function ISOL
Function ISOL(Equatio
by isolating variable.
solve for t in the equa
Using the RPN mod
equation in the stack
ISOL. Right before th
SG49A.book Page 1 Friday, September 16, 2005 1:31 PM
tion of algebraic equations
me of the functions from the Symbolic Solver menu. 
y using the keystroke combination „Î. With 
to CHOOSE boxes, the following menu lists will be 
 
SOLVE can be used to solve for any unknown in a 
. Function SOLVEVX solves a polynomial equation 
is the default CAS variable VX (typically set to ‘X’). 
S provides the zeros, or roots, of a polynomial.
n, variable) will produce the solution(s) to Equation
 For example, with the calculator set to ALG mode, to 
tion at3-bt = 0 we can use the following:
e, the solution is accomplished by entering the 
, followed by the variable, before entering function 
e execution of ISOL, the RPN stack should look as in 
the figure to the left. After applying ISOL, the result is shown in the figure 
to the right: 
 
The first argument in 
equation. For examp
The same problem ca
show the RPN stack b
Function SOLVE
Function SOLVE has t
can also be used to s
entry for function SO
shown next:
NOTE: To type th
(associated with the
SG49A.book Page 2 Friday, September 16, 2005 1:31 PM
Page 6-2
ISOL can be an expression, as shown above, or an 
le, in ALG mode, try:
n be solved in RPN mode as illustrated below (figures 
efore and after the application of function ISOL):
 
he same syntax as function ISOL, except that SOLVE 
olve a set of polynomial equations. The help-facility 
LVE, with the solution to equation X^4 – 1 = 3 , is 
e equal sign (=) in an equation, use ‚Å
 \ key).
Page 6-3
The following examples show the use of function SOLVE in ALG and RPN 
modes (Use Complex mode in the CAS):
The screen shot show
=125, SOLVE produc
SOLVE produces four
solution is not visible 
width of the calculato
by using the down a
operation can be us
calculator’s screen):
The corresponding RP
the application of fun
SG49A.book Page 3 Friday, September 16, 2005 1:31 PM
n above displays two solutions. In the first one, β4-5β
es no solutions { }. In the second one, β4 - 5β = 6, 
 solutions, shown in the last output line. The very last 
because the result occupies more characters than the 
r’s screen. However, you can still see all the solutions 
rrow key (˜), which triggers the line editor (this 
ed to access any output line that is wider than the 
N screens for these two examples, before and after 
ction SOLVE, are shown next:
 
 
Function SOLVEVX
The function SOLVEVX solves an equation for the default CAS variable 
contained in the reserved variable name VX. By default, this variable is set 
to ‘X’. Examples, using the ALG mode with VX = ‘X’, are shown below:
In the first case SOLV
SOLVEVX found a sin
The following screen
shown above (before 
Function ZEROS
The function ZEROS 
showing their multip
expression for the eq
Examples in ALG mod
To use function ZERO
then the variable to 
SG49A.book Page 4 Friday, September 16, 2005 1:31 PM
Page 6-4
EVX could not find a solution. In the second case, 
gle solution, X = 2.
s show the RPN stack for solving the two examples 
and after application of SOLVEVX):
 
 
finds the solutions of a polynomial equation, without 
licity. The function requires having as input the 
uation and the name of the variable to solve for. 
e are shown next:
 
S in RPN mode, enter first the polynomial expression, 
solve for, and then function ZEROS. The following 
Page 6-5
screen shots show the RPN stack before and after the application of 
ZEROS to the two examples above (Use Complex mode in the CAS):
 
The Symbolic Solve
rational equations (m
solved for has all nu
through the use of the
Numerical so
The calculator provid
single algebraic or tr
we start the numer
produces a drop-dow
Following, we prese
finance, and 1. Solv
calculator’s user’s gu
SG49A.book Page 5 Friday, September 16, 2005 1:31 PM
 
r functions presented above produce solutions to 
ainly, polynomial equations). If the equation to be 
merical coefficients, a numerical solution is possible 
 Numerical Solver features of the calculator.
lver menu
es a very powerful environment for the solution of 
anscendental equations. To access this environment 
ical solver (NUM.SLV) by using ‚Ï. This 
n menu that includes the following options:
nt applications of items 3. Solve poly.., 5. Solve 
e equation.., in that order. Appendix 1-A, in the 
ide, contains instructions on how to use input forms 
with examples for the numerical solver applications. Item 6. MSLV
(Multiple equation SoLVer) will be presented later in page 6-10.
Polynomial Equ
Using the Solve poly
can: 
(1) find the solutions t
(2) obtain the coeffici
roots; and, 
(3) obtain an algebra
Finding the solutio
A polynomial equatio
a1x + a0 = 0. For ex
We want to place the
[3,2,0,-1,1]. To solve
the following:
The screen will show 
Notes:
1. Whenever you solve for a value in the NUM.SLV applications, the 
value solved for will be placed in the stack. This is useful if you need to 
keep that value available for other operations.
2. There will be on
some of the applica
‚Ϙ˜@@OK@
„Ô3‚í
‚í1\‚
SG49A.book Page 6 Friday, September 16, 2005 1:31 PM
Page 6-6
ations
…option in the calculator’s SOLVE environment you 
o a polynomial equation;
ents of the polynomial having a number of given 
ic expression for the polynomial as a function of X.
ns to a polynomial equation
n is an equation of the form: anxn + an-1xn-1 + …+ 
ample, solve the equation: 3s4 + 2s3 - s + 1 = 0.
 coefficients of the equation in a vector: 
 for this polynomial equation using the calculator, try 
the solution as follows:
e or more variables created whenever you activate 
tions in the NUM.SLV menu.
@ Select Solve poly…
2‚í0 Enter vector of coefficients
í1@@OK@@ @SOLVE@ Solve equation
Page 6-7
Press ` to return to stack. The stack will show the following results in 
ALG mode (the same result would be shown in RPN mode):
All the solutions are c
0.766, 0.632), (-0.76
Generating polyn
roots
Suppose you want 
numbers [1, 5, -2, 4]
steps: 
Press ` to return to
Press ˜ to trigger t
‚Ϙ˜@@OK
˜„Ô1‚‚í2\‚
SG49A.book Page 7 Friday, September 16, 2005 1:31 PM
omplex numbers: (0.432, -0.389), (0.432, 0.389), (-
6, -0.632).
omial coefficients given the polynomial's 
to generate the polynomial whose roots are the 
. To use the calculator for this purpose, follow these 
 stack, the coefficients will be shown in the stack.
he line editor to see all the coefficients.
@@ Select Solve poly…
í5 Enter vector of roots
í4@@OK@@ @SOLVE@ Solve for coefficients
Generating an algebraic expression for the polynomial
You can use the calculator to generate an algebraic expression for a 
polynomial given the coefficients or the roots of the polynomial. The 
resulting expression will be given in terms of the default CAS variable X.
To generate the algebraic expression using the coefficients, try the 
following example. Assume that the polynomial coefficients are 
[1,5,-2,4]. Use the following keystrokes:
The expression thus 
2*X+4'
To generate the alge
example. Assume th
following keystrokes:
The expression thus g
To expand the produc
The resulting expressi
Financial calcul
The calculations in 
(NUM.SLV) are used 
the discipline of engi
This application can 
„Ò (associated
types of calculations 
guide.
‚Ϙ˜
„Ô1‚í
‚í2\‚
`
‚Ϙ˜@@OK@
˜„Ô1‚
‚í2\‚
`
SG49A.book Page 8 Friday, September 16, 2005 1:31 PM
Page 6-8
generated is shown in the stack as: 'X^3+5*X^2+-
braic expression using the roots, try the following 
at the polynomial roots are [1, 3, -2, 1]. Use the 
enerated is shown in the stack as:
'(X-1)*(X-3)*(X+2)*(X-1)'.
ts, you can use the EXPAND command.
on is: 'X^4+-3*X^3+ -3*X^2+11*X-6'.
ations
item 5. Solve finance.. in the Numerical Solver 
for calculations of time value of money of interest in 
neering economics and other financial applications. 
also be started by using the keystroke combination
 with the 9 key). Detailed explanations of these 
are presented in Chapter 6 of the calculator’s user’s 
Select Solve poly…
5 Enter vector of coefficients
í4@@OK@@—@SYMB@ Generate symbolic expression
Return to stack.
@ Select Solve poly…
í3 Enter vector of roots
í1@@OK@@˜@SYMB@Generate symbolic 
expression
Return to stack.
Page 6-9
Solving equations with one unknown through 
NUM.SLV
The calculator's NUM.SLV menu provides item 1. Solve equation.. solve 
different types of equations in a single variable, including non-linear 
algebraic and transcendental equations. For example, let's solve the 
equation: ex-sin(πx/3) = 0.
Simply enter the ex
variable EQ. The req
³„
*~
Function STEQ
Function STEQ will sto
In RPN mode, ente
command STEQ. Thu
an expression into va
Press J to see the 
Then, enter the SOLVE
‚Ï@@OK@@. The c
SG49A.book Page 9 Friday, September 16, 2005 1:31 PM
pression as an algebraic object and store it into 
uired keystrokes in ALG mode are the following:
¸~„x™-S„ì
„x/3™‚Å0™
K~e~q`
re its argument into variable EQ, e.g., in ALG mode:
r the equation between apostrophes and activate 
s, function STEQ can be used as a shortcut to store 
riable EQ.
newly created EQ variable:
 environment and select Solve equation…, by using:
orresponding screen will be shown as:
The equation we store
the SOLVE EQUATION
solve the equation all
using ˜, and press
This, however, is not t
a negative solution, f
before solving the equ
now X: -3.045.
Solution to sim
Function MSLV is avai
function MSLV is show
Notice that function M
1. A vector containin
2. A vector containin
3. A vector containin
of both X and Y a
SG49A.book Page 10 Friday, September 16, 2005 1:31 PM
Page 6-10
d in variable EQ is already loaded in the Eq field in 
 input form. Also, a field labeled x is provided. To 
 you need to do is highlight the field in front of X: by 
 @SOLVE@. The solution shown is X: 4.5006E-2:
he only possible solution for this equation. To obtain 
or example, enter a negative number in the X: field 
ation. Try 3\ @@@OK@@ ˜ @SOLVE@. The solution is 
ultaneous equations with MSLV
lable in the ‚Ï menu. The help-facility entry for 
n next:
SLV requires three arguments:
g the equations, i.e., ‘[SIN(X)+Y,X+SIN(Y)=1]’
g the variables to solve for, i.e., ‘[X,Y]’
g initial values for the solution, i.e., the initial values 
re zero for this example.
Page 6-11
In ALG mode, press @ECHO to copy the example to the stack, press ` to 
run the example. To see all the elements in the solution you need to 
activate the line editor by pressing the down arrow key (˜):
In RPN mode, the sol
Activating function M
You may have noticed
intermediate informa
provided by MSLV is
shows the results of 
final solution is X = 1
Reference
Additional informatio
in Chapters 6 and 7 
SG49A.book Page 11 Friday, September 16, 2005 1:31 PM
ution for this example is produced by using:
SLV results in the following screen.
 that, while producing the solution, the screen shows 
tion on the upper left corner. Since the solution 
 numerical, the information in the upper left corner 
the iterative process used to obtain a solution. The 
.8238, Y = -0.9681.
n on solving single and multiple equations is provided 
of the calculator’s user’s guide.
SG49A.book Page 12 Friday, September 16, 2005 1:31 PM
Page 7-1
Chapter 7
Operations with lists
Lists are a type of calculator’s object that can be useful for data processing. 
This chapter presents examples of operations with lists. To get started with 
the examples in this Chapter, we use the Approximate mode (See Chapter 
1).
Creating and
To create a list in ALG
or enter the elements
The following keystro
variable L1.
„ä1
Entering the same list
„ä
Operations w
To demonstrate ope
following lists in the c
L2 = {-3.,2.,1.,5.} L3
Changing sign 
The sign-change key 
the sign of all elemen
SG49A.book Page 1 Friday, September 16, 2005 1:31 PM
 storing lists
 mode, first enter the braces key „ä , then type 
 of the list, separating them with commas (‚í). 
kes will enter the list {1.,2.,3.,4.} and store it into 
‚í2‚í3‚í4
™K~l1`
 in RPN mode requires the following keystrokes:
1#2#3#4`
³~l1`K
ith lists of numbers
rations with lists of numbers enter and store the 
orresponding variables.
 = {-6.,5.,3.,1.,0.,3.,-4.} L4 = {3.,-2.,1.,5.,3.,2.,1.}
(\), when applied to a list of numbers, will change 
ts in the list. For example:
Addition, subtraction, multiplication, division
Multiplication and division of a list by a single number is distributed across 
the list, for example:
Subtraction of a sing
from each element in 
Addition of a single 
number, and not an 
list. For example:
Subtraction, multiplic
length produce a lis
Examples: 
SG49A.book Page 2 Friday, September 16, 2005 1:31 PM
Page 7-2
le number from a list will subtract the same number 
the list, for example:
number to a list produces a list augmented by the 
addition of the single number to each element in the 
ation, and division of lists of numbers of the same 
t of the same length with term-by-term operations. 
 
Page 7-3
The division L4/L3 will produce an infinity entry because one of the 
elements in L3 is zero, and an error message is returned. 
If the lists involved 
message (Invalid Dim
The plus sign (+), 
putting together the 
example:
In order to produce t
we need to use opera
function catalog (‚
ADD to add lists L1 a
NOTE: If we had entered the elements in lists L4 and L3 as integers, 
the infinite symbol would be shown whenever a division by zero 
occurs. To produce the following result you need to re-enter the lists as 
integer (remove decimal points) using Exact mode:
SG49A.book Page 3 Friday, September 16, 2005 1:31 PM
in the operation have different lengths, an error 
ensions) is produced.Try, for example, L1-L4.
when applied to lists, acts a concatenation operator, 
two lists, rather than adding them term-by-term. For 
erm-by-term addition of two lists of the same length, 
tor ADD. This operator can be loaded by using the 
N). The screen below shows an application of 
nd L2, term-by-term:
Functions applied to lists
Real number functions from the keyboard (ABS, ex, LN, 10x, LOG, SIN, x2, 
√, COS, TAN, ASIN, ACOS, ATAN, yx) as well as those from the MTH/
HYPERBOLIC menu (SINH, COSH, TANH, ASINH, ACOSH, ATANH), and 
MTH/REAL menu (%, etc.), can be applied to lists, e.g.,
Lists of compl
You can create a com
could enter this as L1
Functions such as LN
complex numbers, e.g
ABS INVERSE (1/x)
SG49A.book Page 4 Friday, September 16, 2005 1:31 PM
Page 7-4
ex numbers
plex number list, say L1 ADD i*L2. In RPN mode, you 
 i L2 ADD *. The result is:
, EXP, SQ, etc., can also be applied to a list of 
.,
 
Page 7-5
Lists of algebraic objects
The following are examples of lists of algebraic objects with the function 
SIN applied to them (select Exact mode for these examples -- See Chapter 
1):
The MTH/LIST
The MTH menu prov
With system flag 117
the following function
With system flag 117
following functions:
The operation of the M
∆LIST: Calc
ΣLIST: Calc
ΠLIST: Calc
SORT: Sorts
REVLIST: Reve
ADD: Ope
lengt
SG49A.book Page 5 Friday, September 16, 2005 1:31 PM
 
 menu
ides a number of functions that exclusively to lists. 
 set to CHOOSE boxes, the MTH/LIST menu offers 
s:
 
 set to SOFT menus, the MTH/LIST menu shows the 
TH/LIST menu is as follows:
ulate increment among consecutive elements in list
ulate summation of elements in the list
ulate product of elements in the list
 elements in increasing order
rses order of list
rator for term-by-term addition of two lists of the same 
h (examples of this operator were shown above)
Examples of application of these functions in ALG mode are shown next:
 
SORT and REVLIST ca
If you are working in
select the operation 
between consecutive 
l
This places L3 onto th
MTH menu.
SG49A.book Page 6 Friday, September 16, 2005 1:31 PM
Page 7-6
 
n be combined to sort a list in decreasing order:
 RPN mode, enter the list onto the stack and then 
you want. For example, to calculate the increment 
elements in list L3, press:
3`!´˜˜#OK# #OK#
e stack and then selects the ∆LIST operation from the 
Page 7-7
The SEQ function
The SEQ function, available through the command catalog (‚N), 
takes as arguments an expression in terms of an index, the name of the 
index, and starting, ending, and increment values for the index, and 
returns a list consisting of the evaluation of the expression for all possible 
values of the index. The general form of the function is
SEQ(e
For example:
The list produced cor
The MAP func
The MAP function, a
takes as arguments a
list consisting of the a
example, the followin
the list {1,2,3}:
In ALG mode, the syn
~~map~
In RPN mode, the syn
!ä1@í
In both cases, you 
examples above) or s
Reference
For additional referen
8 in the calculator’s u
SG49A.book Page 7 Friday, September 16, 2005 1:31 PM
xpression, index, start, end, increment)
responds to the values {12, 22, 32, 42}.
tion
vailable through the command catalog (‚N), 
 list of numbers and a function f(X), and produces a 
pplication of that function to the list of numbers. For 
g call to function MAP applies the function SIN(X) to 
tax is:
!Ü!ä1@í2@í3™
@íS~X`
tax is:
2@í3`³S~X`~
~map`
can either type out the MAP command (as in the 
elect the command from the CAT menu.
ces, examples, and applications of lists see Chapter 
ser’s guide.
SG49A.book Page 8 Friday, September 16, 2005 1:31 PM
Page 8-1
Chapter 8
Vectors
This Chapter provides examples of entering and operating with vectors, 
both mathematical vectors of many elements, as well as physical vectors of 
2 and 3 components.
Entering vecto
In the calculator, ve
enclosed between b
brackets are genera
„Ô, associated
vectors in the calcula
Typing vectors i
With the calculator 
opening a set of b
elements of the vecto
below show the ente
vector. The figure to
`. The figure to the
algebraic vector:
In RPN mode, you c
brackets and typing th
commas (‚í) o
either mode, the ca
spaces.
[3.5, 2.2, -1.
[1.5,-2.2]
[3,-1,2]
['t','t^2','SI
SG49A.book Page 1 Friday, September 16, 2005 1:31 PM
rs 
ctors are represented by a sequence of numbers 
rackets, and typically entered as row vectors. The 
ted in the calculator by the keystroke combination 
 with the * key. The following are examples of 
tor:
n the stack
in ALG mode, a vector is typed into the stack by 
rackets („Ô) and typing the components or 
r separated by commas (‚í). The screen shots 
ring of a numerical vector followed by an algebraic 
 the left shows the algebraic vector before pressing 
 right shows the calculator’s screen after entering the 
 
an enter a vector in the stack by opening a set of 
e vector components or elements separated by either 
r spaces (#). Notice that after pressing `, in 
lculator shows the vector elements separated by 
3, 5.6, 2.3] A general row vector
A 2-D vector
A 3-D vector
N(t)'] A vector of algebraics
Storing vectors into variables in the stack
Vectors can be stored into variables. The screen shots below show the 
vectors
u2 = [1, 2], u3 = [-3, 2, -2], v2 = [3,-1], v3 = [1, -5, 2]
Stored into variables @@@u2@@, @@@u3@@, @@@v2@@, and @@@v3@@, respectively. First, in 
ALG mode:
Then, in RPN mode (b
NOTE: The apostro
names u2, v2, etc
overwrite the existin
apostrophes must 
previously.
SG49A.book Page 2 Friday, September 16, 2005 1:31 PM
Page 8-2
 
efore pressing K, repeatedly):
 
phes (‘) are not needed ordinarily in entering the 
. in RPN mode. In this case, they are used to 
g variables created earlier in ALG mode. Thus, the 
be used if the existing variables are not purged 
Page 8-3
Using the Matrix Writer (MTRW) to enter vectors
Vectors can also be entered by using the Matrix Writer „² (third key 
in the fourth row of keys from the top of the keyboard). This command 
generates a species of spreadsheet corresponding to rows and columns of 
a matrix (Details on using the Matrix Writer to enter matrices will be 
presented in Chapter 9). For a vector we are interested in filling only 
elements in the top row. By default, the cell in the top row and first column 
is selected. At the bo
menu keys:
@EDI
The @EDIT key is us
Writer.
The key, w
matrix of one row
The key is 
spreadsheet. Pres
decrease in your M
The key is 
spreadsheet. Press
increase in your M
The key, w
right of the current
default. This optio
elements.
The key, wh
the current cell wh
be selected before
Activate the Matrix W
check out the second
show the keys:
Moving to the ri
Activate the Matrix
with the key
of numbers with th
first case you enter
you entered a matri
SG49A.book Page 3 Friday, September 16, 2005 1:31 PM
ttom of the spreadsheet you will find the following soft 
T! 
ed to edit the contents of a selected cell in the Matrix 
hen selected, will produce a vector, as opposed to a 
 and many columns.
used to decrease the width of the columns in the 
s this key a couple of times to see the column width 
atrix Writer.
used to increase the width of the columns in the 
 this key a couple of times to see the column width 
atrix Writer.
hen selected, automatically selects the next cell to the 
 cell when you press `. This option is selected by 
n, if desired, needs to be selected before entering 
en selected, automatically selects the next cell below 
en you press `. This option,if desired, needs to 
 entering elements.
riter again by using „², and press L to 
 soft key menu at the bottom of the display. It will 
ght vs. moving down in the Matrix Writer
 Writer and enter 3`5`2``
 selected (default). Next, enter the same sequence 
e key selected to see the difference. In the 
ed a vector of three elements. In the second case 
x of three rows and one column.
@+ROW@ @-ROW @+COL@ @-COL@ @GOTO@
The @+ROW@ key will add a row full of zeros at the location of the selected 
cell of the spreadsheet.
The @-ROW key will delete the row corresponding to the selected cell of 
the spreadsheet.
The @+COL@ key will add a column full of zeros at the location of the 
selected cell of the spreadsheet.
The @-COL@ key will
of the spreadshee
The key will
The @GOTO@ key, wh
number of the row
cursor.
Pressing L once m
function @@DEL@ (delete)
The function @@DEL@ 
replace it with a z
To see these keys in a
(1) Activate the Matrix
and keys a
(2) Enter the following
L
(3) Move the cursor u
The second row w
(4) Press @+ROW@. A row
(5) Press @-COL@. The f
(6) Press @+COL@. A co
(7) Press @GOTO@ 3 @@
(8) Press . This 
although you will 
normal display. T
entered will be av
SG49A.book Page 4 Friday, September 16, 2005 1:31 PM
Page 8-4
 delete the column corresponding to the selected cell 
t.
 place the contents of the selected cell on the stack.
en pressed, will request that the user indicate the 
 and column where he or she wants to position the 
ore produces the last menu, which contains only one 
.
will delete the contents of the selected cell and 
ero.
ction try the following exercise:
 Writer by using „². Make sure the 
re selected.
:
1`2`3`
 @GOTO@ 2 @@OK@@ 1 @@OK@@ @@OK@@
4`5`6`
7`8`9`
p two positions by using ——. Then press @-ROW. 
ill disappear.
 of three zeroes appears in the second row.
irst column will disappear.
lumn of two zeroes appears in the first column.
OK@@ 3 @@OK@@ @@OK@@ to move to position (3,3). 
will place the contents of cell (3,3) on the stack, 
not be able to see it yet. Press ` to return to 
he number 9, element (3,3), and the full matrix 
ailable in the stack.
Page 8-5
Simple operations with vectors
To illustrate operations with vectors we will use the vectors u2, u3, v2, and 
v3, stored in an earlier exercise. Also, store vector A=[-1,-2,-3,-4,-5] to be 
used in the following exercises.
Changing sign
To change the sign o
Addition, subtra
Addition and subtrac
have the same length
Attempting to add or
message:
SG49A.book Page 5 Friday, September 16, 2005 1:31 PM
f a vector use the key \, e.g., 
ction
tion of vectors require that the two vector operands 
:
 subtract vectors of different length produces an error 
Multiplication by a scalar, and division by a scalar
Multiplication by a scalar or division by a scalar is straightforward:
Absolute value 
The absolute value fu
magnitude of the vec
ABS(u3), will show
The MTH/VEC
The MTH menu („
vector objects:
The VECTOR menu co
CHOOSE boxes):
SG49A.book Page 6 Friday, September 16, 2005 1:31 PM
Page 8-6
 
function
nction (ABS), when applied to a vector, produces the 
tor. For example: ABS([1,-2,6]), ABS(A), 
 in the screen as follows:
TOR menu
´) contains a menu of functions that specifically to 
ntains the following functions (system flag 117 set to 
Page 8-7
 
Magnitude
The magnitude of a v
ABS. This function
Examples of applicat
Dot product 
Function DOT (option
dot product of two 
application of functio
stored earlier, are sho
product of two vector
Cross product
Function CROSS (opt
the cross product of tw
one 3-D vector. For
vector of the form 
Examples in ALG mo
Notice that the cross 
z-direction only, i.e., a
SG49A.book Page 7 Friday, September 16, 2005 1:31 PM
ector, as discussed earlier, can be found with function 
 is also available from the keyboard („Ê). 
ion of function ABS were shown above.
 2 in CHOOSE box above) is used to calculate the 
vectors of the same length. Some examples of 
n DOT, using the vectors A, u2, u3, v2, and v3, 
wn next in ALG mode. Attempts to calculate the dot 
s of different length produce an error message:
 
ion 3 in the MTH/VECTOR menu) is used to calculate 
o 2-D vectors, of two 3-D vectors, or of one 2-D and 
 the purpose of calculating a cross product, a 2-D 
[Ax, Ay], is treated as the 3-D vector [Ax, Ay,0]. 
de are shown next for two 2-D and two 3-D vectors. 
product of two 2-D vectors will produce a vector in the 
 vector of the form [0, 0, Cz]:
 
Examples of cross products of one 3-D vector with one 2-D vector, or vice 
versa, are presented 
Attempts to calculate 
produce an error mes
Reference
Additional informatio
in the physical scienc
guide.
SG49A.book Page 8 Friday, September 16, 2005 1:31 PM
Page 8-8
next:
a cross product of vectors of length other than 2 or 3, 
sage:
n on operations with vectors, including applications 
es, is presented in Chapter 9 of the calculator’s user’s 
Page 9-1
Chapter 9
Matrices and linear algebra
This chapter shows examples of creating matrices and operations with 
matrices, including linear algebra applications.
Entering matrices in the stack
In this section we pr
calculator stack: (1) 
directly into the stack
Using the Matri
As with the case of
entered into the stack
matrix:
first, start the Matrix W
 is selected. T
2.5\
.3
2
At this point, the Mat
Press ` once mor
stack is shown next, b
SG49A.book Page 1 Friday, September 16, 2005 1:31 PM
esent two different methods to enter matrices in the 
using the Matrix Writer, and (2) typing the matrix 
.
x Writer
 vectors, discussed in Chapter 8, matrices can be 
 by using the Matrix Writer. For example, to enter the 
riter by using „². Make sure that the option 
hen use the following keystrokes:
`4.2`2`˜ššš
`1.9`2.8`
`.1\`.5`
rix Writer screen looks like this:
e to place the matrix on the stack. The ALG mode 
efore and after pressing `, once more:
,
5.01.02
8.29.13.0
0.22.45.2
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
−
−
 
If you have selected the textbook display option (using H@)DISP! and 
checking off �Textb
Otherwise, the displa
The display in RPN m
Typing in the m
The same result as 
directly into the stack
„Ô
„Ô2.5
‚í
„Ô.3‚
‚í
„Ô2‚í
Thus, to enter a ma
(„Ô) and enclo
brackets („Ô).
elements of each row
For future exercises, le
use K~a. In R
SG49A.book Page 2 Friday, September 16, 2005 1:31 PM
Page 9-2
ook), the matrix will look like the one shown above. 
y will show:
ode will look very similar to these.
atrix directly into the stack
above can be achieved by entering the following 
:
\‚í4.2‚í2™
í1.9‚í2.8™
.1\‚í.5`
trix directly into the stack open a set of brackets 
se each row of the matrix with an additional set of 
 Commas (‚í.) should separate the 
, as well as the brackets between rows.
t’s save this matrix under the name A. In ALG mode 
PN mode, use ³~aK.
Page 9-3
Operations with matrices
Matrices, like other mathematical objects, can be added and subtracted. 
They can be multiplied by a scalar, or among themselves, and raised to a 
real power. An important operation for linear algebra applications is the 
inverse of a matrix. Details of these operations are presented next.
To illustrate the operations we will create a number of matrices that we will 
store in the following
B23, A33 and B33
different):
In RPN mode, the ste
{2,2}` RANM '
{2,3}` RANM '
{3,2}` RANM '
{3,3}` RANM '
SG49A.book Page 3 Friday, September 16, 2005 1:31 PM
 variables. Here are the matrices A22, B22, A23, 
 (The random matrices in your calculator may beps to follow are: 
A22'`K{2,2}` RANM 'B22'`K
A23'`K{2,3}` RANM 'B23'`K
A32'`K{3,2}` RANM 'B32'`K
A33'`K{3,3}` RANM 'B33'`K
Addition and subtraction
Four examples are shown below using the matrices stored above (ALG 
mode).
In RPN mode, try the 
Multiplication
There are a number
These are described n
Multiplication by a
Some examples of mu
A22 ` B22`+
A23 ` B23`+
A32 ` B32`+
A33 ` B33`+
SG49A.book Page 4 Friday, September 16, 2005 1:31 PM
Page 9-4
 
following eight examples:
 of multiplication operations that involve matrices. 
ext. The examples are shown in algebraic mode.
 scalar
ltiplication of a matrix by a scalar are shown below.
 
A22 ` B22`-
A23 ` B23`-
A32 ` B32`-
A33 ` B33`-
Page 9-5
Matrix-vector multiplication
Matrix-vector multiplication is possible only if the number of columns of the 
matrix is equal to the length of the vector. A couple of examples of matrix-
vector multiplication follow: 
Vector-matrix multipli
multiplication can be
multiplication as defin
Matrix multiplicat
Matrix multiplication 
multiplication is only 
is equal to the numbe
the product, cij, is def
Matrix multiplication
Furthermore, one of t
screen shots show th
stored earlier:
1
c
p
k
ij =∑
=
SG49A.book Page 5 Friday, September 16, 2005 1:31 PM
 
cation, on the other hand, is not defined. This 
 performed, however, as a special case of matrix 
ed next. 
ion
is defined by Cm×n = Am×p⋅Bp×n. Notice that matrix 
possible if the number of columns in the first operand 
r of rows of the second operand. The general term in 
ined as 
 is not commutative, i.e., in general, A⋅B ≠ B⋅A. 
he multiplications may not even exist. The following 
e results of multiplications of the matrices that we 
 
.,,2,1;,,2,1, njmiforba kjik KK ==⋅
Term-by-term multiplication
Term-by-term multiplication of two matrices of the same dimensions is 
possible through the use of function HADAMARD. The result is, of course, 
another matrix of the same dimensions. This function is available through 
Function catalog (‚N), or through the MATRICES/OPERATIONS sub-
menu („Ø). Applications of function HADAMARD are presented 
next: 
Raising a matrix t
You can raise a mat
integer or a real nu
shows the result of ra
You can also raise a 
In algebraic mode, 
[enter the power] `
In RPN mode, the key
power] Q`.
SG49A.book Page 6 Friday, September 16, 2005 1:31 PM
Page 9-6
 
o a real power
rix to any power as long as the power is either an 
mber with no fractional part. The following example 
ising matrix B22, created earlier, to the power of 5:
matrix to a power without first storing it as a variable:
the keystrokes are: [enter or select the matrix] Q
.
strokes are: [enter or select the matrix] † [enter the 
Page 9-7
The identity matrix
The identity matrix has the property that A⋅I = I⋅A = A. To verify this 
property we present the following examples using the matrices stored 
earlier on. Use function IDN (find it in the MTH/MATRIX/MAKE menu) to 
generate the identity matrix as shown here:
The inverse matrix
The inverse of a squa
= I, where I is the ide
of a matrix is obtaine
(i.e., the Y key). E
earlier are presented 
To verify the proper
multiplications:
SG49A.book Page 7 Friday, September 16, 2005 1:31 PM
 
re matrix A is the matrix A-1 such that A⋅A-1 = A-1⋅A
ntity matrix of the same dimensions as A. The inverse 
d in the calculator by using the inverse function, INV 
xamples of the inverse of some of the matrices stored 
next:
 
ties of the inverse matrix, we present the following 
 
Characterizing a matrix (The matrix NORM 
menu)
The matrix NORM (NORMALIZE) menu is accessed through the keystroke 
sequence „´. This menu is described in detail in Chapter 10 of the 
calculator’s user’s guide. Some of these functions are described next. 
Function DET
Function DET calculat
Function TRACE
Function TRACE calcu
of the elements in its 
Examples:
SG49A.book Page 8 Friday, September 16, 2005 1:31 PM
Page 9-8
es the determinant of a square matrix. For example,
 
lates the trace of square matrix, defined as the sum 
main diagonal, or
.
 
∑
=
=
n
i
iiatr
1
)(A
Page 9-9
Solution of linear systems
A system of n linear equations in m variables can be written as
a11⋅x1 + a12⋅x2 + a13⋅x3 + …+ a1,m-1⋅x m-1 + a1,m⋅x m = b1,
a21⋅x1 + a22⋅x2 + a23⋅x3 + …+ a2,m-1⋅x m-1 + a2,m⋅x m = b2,
a31⋅x1 + a32⋅x2 + a33⋅x3 + …+ a3,m-1⋅x m-1 + a3,m⋅x m = b3,
. . . 
an-1,1⋅x1 + an-1,2⋅x
an1⋅x1 + an2⋅x2 +
This system of linea
An×m⋅xm×1 = bn×1, if
Using the nume
There are many wa
calculator. One poss
the numerical solver s
lin sys.., and press @@@O
To solve the linear sys
[[ a11, a12, … ], … [
field. When the X:
available, the solution
also copied to stack l
The system of linear e
nn
aa
aa
aa
A
⎢
⎢
⎢
⎢
⎣
⎡
=
MM
1
221
111
SG49A.book Page 9 Friday, September 16, 2005 1:31 PM
 … . . .
2 + an-1,3⋅x3 + …+ an-1,m-1⋅x m-1 + an-1,m⋅x m = bn-1,
 an3⋅x3 + …+ an,m-1⋅x m-1 + an,m⋅x m = bn.
r equations can be written as a matrix equation, 
 we define the following matrix and vectors:
, , 
rical solver for linear systems
ys to solve a system of linear equations with the 
ibility is through the numerical solver ‚Ï. From 
creen, shown below (left), select the option 4. Solve 
K@@@. The following input form will be provide (right):
 
tem A⋅x = b, enter the matrix A, in the format 
….]] in the A: field. Also, enter the vector b in the B: 
 field is highlighted, press @SOLVE. If a solution is 
 vector x will be shown in the X: field. The solution is 
evel 1. Some examples follow.
quations
mn
nm
m
m
a
a
a
×
⎥
⎥
⎥
⎥
⎦
⎤
L
MO
L
L
2
22
12
1
2
1
×
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
=
m
m
x
x
x
x
M
1
2
1
×
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
=
n
n
b
b
b
b
M
2x1 + 3x2 –5x3 = 13,
x1 – 3x2 + 8x3 = -13,
2x1 – 2x2 + 4x3 = -6,
can be written as the matrix equation A⋅x = b, if 
This system has the sa
referred to as a squ
solution to the system
three planes in the co
equations.
To enter matrix A yo
selected. The followi
matrix A, as well as 
matrix A (press ` 
Press ˜ to select t
vector with a single s
After entering matrix 
can press @SOLVE! to at
13
2
1
532
1 ⎤⎡⎤⎡⎤
⎢
⎢
⎢
⎣
⎡
−
−
−
=A
x
SG49A.book Page 10 Friday, September 16, 2005 1:31 PM
Page 9-10
me number of equations as of unknowns, and will be 
are system. In general, there should be a unique 
. The solution will be the point of intersection of the 
ordinate system (x1, x2, x3) represented by the three 
u can activate the Matrix Writer while the A: field is 
ng screen shows the Matrix Writer used for entering 
the input form for the numerical solver after entering 
in the Matrix Writer):
 
he B: field. The vector b can be entered as a row 
et of brackets, i.e., [13,-13,-6] @@@OK@@@ .
A and vector b, and with the X: field highlighted, we 
tempt a solution to this system of equations:
.
6
13,,
42
83
3
2
⎥
⎥
⎥
⎦⎢
⎢
⎢
⎣ −
−=
⎥
⎥
⎥
⎦⎢
⎢
⎢
⎣
=
⎥
⎥
⎥
⎦
bx and
x
x
Page 9-11
A solution was found as shown next.
Solution with th
The solution to the sys
x = A-1⋅ b. For the 
calculator as follows 
Solution by “div
While the operation 
calculator’s / key 
matrix equation A⋅x 
is illustrated below fo
The procedure is sho
and vector b once m
SG49A.book Page 11 Friday, September 16, 2005 1:31 PM
e inversematrix
tem A⋅x = b, where A is a square matrix is 
example used earlier, we can find the solution in the 
(First enter matrix A and vector b once more):
 
ision” of matrices
of division is not defined for matrices, we can use the 
to “divide” vector b by matrix A to solve for x in the 
= b. The procedure for the case of “dividing” b by A
r the example above.
wn in the following screen shots (type in matrices A
ore):
 
References
Additional information on creating matrices, matrix operations, and matrix 
applications in linear algebra is presented in Chapters 10 and 11 of the 
calculator’s user’s guide.
SG49A.book Page 12 Friday, September 16, 2005 1:31 PM
Page 9-12
Page 10-1
Chapter 10
Graphics
In this chapter we introduce some of the graphics capabilities of the 
calculator. We will present graphics of functions in Cartesian coordinates 
and polar coordinates, parametric plots, graphics of conics, bar plots, 
scatterplots, and fast 3D plots.
Graphs optio
To access the list of 
keystroke sequence „
RPN mode these two
of the graph function
will produce the PLO
illustrated below.
Right in front of the T
highlighted. This is th
list of available grap
will produce a drop d
down-arrow keys to s
SG49A.book Page 1 Friday, September 16, 2005 1:31 PM
ns in the calculator
graphic formats available in the calculator, use the 
ô(D) Please notice that if you are using the 
 keys must be pressed simultaneously to activate any 
s. After activating the 2D/3D function, the calculator 
T SETUP window, which includes the TYPE field as 
YPE field you will, most likely, see the option Function
e default type of graph for the calculator. To see the 
h types, press the soft menu key labeled @CHOOS. This 
own menu with the following options (use the up- and 
ee all the options):
 
Plotting an ex
As an example, let's 
• First, enter the PLO
sure that the optio
selected as the ind
return to normal ca
look similar to this
• Enter the PLOT env
simultaneously if in
writer. You will be
Y1(x) = �. Type th
shows the followin
SG49A.book Page 2 Friday, September 16, 2005 1:31 PM
Page 10-2
pression of the form y = f(x)
plot the function,
T SETUP environment by pressing, „ô. Make 
n Function is selected as the TYPE, and that ‘X’ is 
ependent variable (INDEP). Press L@@@OK@@@ to 
lculator display. The PLOT SET UP window should 
:
ironment by pressing „ñ(press them 
 RPN mode). Press @ADD to get you into the equation 
 prompted to fill the right-hand side of an equation 
e function to be plotted so that the Equation Writer 
g:
)
2
exp(
2
1
)(
2x
xf −=
π
Page 10-3
• Press ` to return to the PLOT - FUNCTION window. The expression 
‘Y1(X) = EXP(-X^2/2)/√(2*π)’ will be highlighted. Press L@@@OK@@@ to 
return to normal calculator display.
• Enter the PLOT WINDOW environment by entering „ò (press 
them simultaneously if in RPN mode). Use a range of –4 to 4 for H-
VIEW, then press @AUTO to generate the V-VIEW automatically. The PLOT 
WINDOW screen looks as follows:
• Plot the graph: @ER
• To see labels: @EDI
• To recover the first
• To trace the curve:
(š™) to move 
trace will be show
1.05 , y = 0.0231
picture of the grap
• To recover the me
press L@CANCL. 
SG49A.book Page 3 Friday, September 16, 2005 1:31 PM
ASE @DRAW (wait till the calculator finishes the graphs)
T L @LABEL @MENU
 graphics menu: LL@)PICT
 @TRACE @@X,Y@@ . Then use the right- and left-arrow keys 
about the curve. The coordinates of the points you 
n at the bottom of the screen. Check that for x = 
. Also, check that for x = -1.48 , y = 0.134. Here is 
h in tracing mode:
nu, and return to the PLOT WINDOW environment, 
Press L@@OK@@ to return to normal display.
Generating a table of values for a function
The combinations „õ(E) and „ö(F), pressed 
simultaneously if in RPN mode, let’s the user produce a table of values of 
functions. For example, we will produce a table of the function Y(X) = X/
(X+10), in the range -5 < X < 5 following these instructions:
• We will generate values of the function f(x), defined above, for values 
of x from –5 to 5, 
graph type is set t
press them simulta
Type option will b
FUNCTION, pres
option, then press 
• Next, press ˜ to
the function expre
• To accept the chan
You will be returne
• The next step is to 
combination „õ
mode. This will pr
value (Start) and t
@@@OK@@@ 0.5
Toggle the 
the option Small F
you to normal calc
• To see the table, p
simultaneously if in
= -5, -4.5, …, and
default. You can u
table. You will no
for the independe
maximum value fo
Some options availab
• The @DEFN, when se
variable.
• The @@BIG@ key simp
vice versa. Try it. 
• The @ZOOM key, whe
Out, Decimal, Inte
SG49A.book Page 4 Friday, September 16, 2005 1:31 PM
Page 10-4
in increments of 0.5. First, we need to ensure that the 
o FUNCTION in the PLOT SETUP screen („ô, 
neously, if in RPN mode). The field in front of the 
e highlighted. If this field is not already set to 
s the soft key @CHOOS and select the FUNCTION 
@@@OK@@@.
 highlight the field in front of the option EQ, and type 
ssion: ‘X/(X+10)’. Press `.
ges made to the PLOT SETUP screen press L@@@OK@@@. 
d to normal calculator display.
access the Table Set-up screen by using the keystroke 
 (i.e., soft key E) – simultaneously if in RPN 
oduce a screen where you can select the starting 
he increment (Step). Enter the following: 5\ 
 @@@OK@@@0.5 @@@OK@@@ (i.e., Zoom factor = 0.5). 
soft menu key until a check mark appears in front of 
ont if you so desire. Then press @@@OK@@@. This will return 
ulator display.
ress „ö(i.e., soft menu key F) – 
 RPN mode. This will produce a table of values of x 
 the corresponding values of f(x), listed as Y1 by 
se the up and down arrow keys to move about in the 
tice that we did not have to indicate an ending value 
nt variable x. Thus, the table continues beyond the 
r x suggested early, namely x = 5.
le while the table is visible are @ZOOM, @@BIG@, and @DEFN:
lected, shows the definition of the independent 
ly changes the font in the table from small to big, and 
n pressed, produces a menu with the options: In, 
ger, and Trig. Try the following exercises:
Page 10-5
• With the option In highlighted, press @@@OK@@@. The table is expanded 
so that the x-increment is now 0.25 rather than 0.5. Simply, what 
the calculator does is to multiply the original increment, 0.5, by the 
zoom factor, 0.5, to produce the new increment of 0.25. Thus, the 
zoom in option is useful when you want more resolution for the 
values of x in your table.
• To increase the resolution by an additional factor of 0.5 press @ZOOM, 
select In once
0.0125.
• To recover the
the option Un-z
• To recover the
again, or use t
• The option Dec
• The option Inte
• The option Trig
being useful w
• To return to no
Fast 3D plots
Fast 3D plots are use
by equations of the fo
= f(x,y) = x2+y2, we 
• Press „ô, sim
SETUP window. 
• Change TYPE to 
• Press ˜ and typ
• Make sure that ‘X’
variables.
• Press L@@@OK@@@ to
• Press „ò, sim
WINDOW screen
SG49A.book Page 5 Friday, September 16, 2005 1:31 PM
 more, and press @@@OK@@@. The x-increment is now 
 previous x-increment, press @ZOOM —@@@OK@@@ to select 
oom. The x-increment is increased to 0.25.
 original x-increment of 0.5 you can do an un-zoom
he option zoom out by pressing @ZOOM ˜@@@OK@@@.
imal in @ZOOM produces x-increments of 0.10.
ger in @ZOOM produces x-increments of 1.
 in produces increments related to fractions of π, thus 
hen producing tables of trigonometric functions.
rmal calculator display press `.
d to visualize three-dimensional surfaces represented 
rm z = f(x,y). For example, if you want to visualizez 
can use the following:
ultaneously if in RPN mode, to access to the PLOT 
Fast3D. ( @CHOOS!, find Fast3D, @@OK@@).
e ‘X^2+Y^2’ @@@OK@@@.
 is selected as the Indep: and ‘Y’ as the Depnd: 
 return to normal calculator display.
ultaneously if in RPN mode, to access the PLOT 
. 
• Keep the default plot window ranges to read:
• Press @ERASE @DRAW t
wireframe picture 
shown at the lowe
(š™—˜) y
orientation of the r
Try changing the s
show a couple of 
• When done, press
• Press @CANCL to retu
• Change the Step d
• Press @ERASE @DRAW 
X-Left:-1 X-Right:1
Y-Near:-1 Y-Far: 1
Z-Low: -1 Z-High: 1
Step Indep: 10 Depnd: 8
NOTE: The Step In
gridlines to be used
is to produce the 
generation are rela
values of 10 and 8
SG49A.book Page 6 Friday, September 16, 2005 1:31 PM
Page 10-6
o draw the three-dimensional surface. The result is a 
of the surface with the reference coordinate system 
r left corner of the screen. By using the arrow keys 
ou can change the orientation of the surface. The 
eference coordinate system will change accordingly. 
urface orientation on your own. The following figures 
views of the graph:
 
 @EXIT.
rn to the PLOT WINDOW environment. 
ata to read: Step Indep: 20 Depnd: 16
to see the surface plot. Sample views:
 
dep: and Depnd: values represent the number of 
 in the plot. The larger these number, the slower it 
graph, although, the times utilized for graphic 
tively fast. For the time being we’ll keep the default 
 for the Step data.
Page 10-7
• When done, press @EXIT.
• Press @CANCL to return to PLOT WINDOW.
• Press $, or L@@@OK@@@, to return to normal calculator display.
Try also a Fast 3D plot for the surface z = f(x,y) = sin (x2+y2)
• Press „ô, simultaneously if in RPN mode, to access the PLOT 
SETUP window.
• Press ˜ and typ
• Press @ERASE @DRAW 
@)LABEL @MENU to see
identifying labels.
• Press LL@)PIC
• Press @CANCL to retu
$, or L@@@OK@@
Reference
Additional informatio
the calculator’s user’s
SG49A.book Page 7 Friday, September 16, 2005 1:31 PM
e ‘SIN(X^2+Y^2)’ @@@OK@@@.
to draw the slope field plot. Press @EXIT @EDIT L 
 the plot unencumbered by the menu and with 
T to leave the EDIT environment.
rn to the PLOT WINDOW environment. Then, press 
@, to return to normal calculator display.
n on graphics is available in Chapters 12 and 22 in 
 guide.
SG49A.book Page 8 Friday, September 16, 2005 1:31 PM
Page 11-1
Chapter 11
Calculus Applications
In this Chapter we discuss applications of the calculator’s functions to 
operations related to Calculus, e.g., limits, derivatives, integrals, power 
series, etc.
The CALC (Ca
Many of the functio
calculator’s CALC m
„Ö (associated 
The first four options 
derivatives and inte
equations, and (4) g
presented in this Cha
page 11-3, respective
Limits and de
Differential calculus d
and their applicatio
function is defined as
in the independent va
continuity of functions
Function lim
The calculator provid
function uses as inpu
where the limit is to 
command catalog (‚
SERIES… of the CALC
SG49A.book Page 1 Friday, September 16, 2005 1:31 PM
lculus) menu
ns presented in this Chapter are contained in the 
enu, available through the keystroke sequence 
with the 4 key):
in this menu are actually sub-menus that apply to (1) 
grals, (2) limits and power series, (3) differential 
raphics. The functions in entries (1) and (2) will be 
pter. Functions DERVX and INTVX are discussed in 
ly.
rivatives
eals with derivatives, or rates of change, of functions 
ns in mathematical analysis. The derivative of a 
 a limit of the difference of a function as the increment 
riable tends to zero. Limits are used also to check the 
.
es function lim to calculate limits of functions. This 
t an expression representing a function and the value 
be calculated. Function lim is available through the 
N~„l) or through option 2. LIMITS & 
 menu (see above). 
Function lim is entered in ALG mode as lim(f(x),x=a) to calculate 
the limit . In RPN mode, enter the function first, then the 
expression ‘x=a’, and finally function lim. Examples in ALG mode are 
shown next, including some limits to infinity, and one-sided limits. The 
infinity symbol is associated with the 0 key, i.e.., „è.
To calculate one-side
“+0” means limit from
example, the limit o
determined with the f
‚N~
1™
The result is as follow
)(lim xf
ax→
SG49A.book Page 2 Friday, September 16, 2005 1:31 PM
Page 11-2
 
d limits, add +0 or -0 to the value to the variable. A 
 the right, while a “–0” means limit from the left. For 
f as x approaches 1 from the left can be 
ollowing keystrokes (ALG mode):
„l˜$OK$ R!ÜX-
@íX@Å1+0`
s:
1−x
Page 11-3
Functions DERIV and DERVX
The function DERIV is used to take derivatives in terms of any independent 
variable, while the function DERVX takes derivatives with respect to the 
CAS default variable VX (typically ‘X’). While function DERVX is available 
directly in the CALC menu, both functions are available in the 
DERIV.&INTEG sub-menu within the CALCL menu ( „Ö).
Function DERIV requires a function, say f(t), and an independent variable, 
say, t, while function 
shown next in ALG m
entered before the fun
Anti-derivativ
An anti-derivative of a
One way to represen
if and only if, f(x) = d
Functions INT, I
The calculator prov
SIGMAVX to calculat
and SIGMA work w
and SIGMAVX utiliz
Functions INT and RIS
function being integ
Function INT, require
evaluated. Functions 
the function to integra
and SIGMAVX are av
is available in the co
ALG mode (type the f
SG49A.book Page 3 Friday, September 16, 2005 1:31 PM
DERVX requires only a function of VX. Examples are 
ode. Recall that in RPN mode the arguments must be 
ction is applied.
 
es and integrals
 function f(x) is a function F(x) such that f(x) = dF/dx. 
t an anti-derivative is as a indefinite integral, i.e.,
F/dx, and C = constant.
NTVX, RISCH, SIGMA and SIGMAVX
ides functions INT, INTVX, RISCH, SIGMA and 
e anti-derivatives of functions. Functions INT, RISCH, 
ith functions of any variable, while functions INTVX, 
e functions of the CAS variable VX (typically, ‘x’). 
CH require, therefore, not only the expression for the 
rated, but also the independent variable name. 
s also a value of x where the anti-derivative will be 
INTVX and SIGMAVX require only the expression of 
te in terms of VX. Functions INTVX, RISCH, SIGMA 
ailable in the CALC/DERIV&INTEG menu, while INT 
mmand catalog. Some examples are shown next in 
unction names to activate them):
CxFdxxf +=∫ )()(
 
Please notice that f
integrands that involv
function shown above
one defined for integ
Definite integra
In a definite integral 
at the upper and low
subtracted. Symbolica
The PREVAL(f(x),a,b) 
returning f(b)-f(a) with
SG49A.book Page 4 Friday, September 16, 2005 1:31 PM
Page 11-4
 
unctions SIGMAVX and SIGMA are designed for 
e some sort of integer function like the factorial (!) 
. Their result is the so-called discrete derivative, i.e., 
er numbers only.
ls
of a function, the resulting anti-derivative is evaluated 
er limit of an interval (a,b) and the evaluated values 
lly, where f(x) = dF/dx. 
function of the CAS can simplify such calculation by 
 x being the CAS variable VX.
),()()( aFbFdxxf
b
a
−=∫
Page 11-5
Infinite series
A function f(x) can be expanded into an infinite series around a point x=x0
by using a Taylor’s series, namely,
,
where f(n)(x) represen
f(x).
If the value x0 = 0, th
Functions TAYLR
Functions TAYLR, TA
polynomials, as well 
available in the CA
Chapter.
Function TAYLOR0 pe
0, of an expression i
The expansion uses
between the highesta
Function TAYLR produ
variable x about a p
the function has the fo
Function SERIES prod
function f(x) to be e
∑
∞
=
−⋅=
0
)(
)(
!
)(
)(
n
n
o
o
n
xx
n
xf
xf
SG49A.book Page 5 Friday, September 16, 2005 1:31 PM
ts the n-th derivative of f(x) with respect to x, f(0)(x) = 
e series is referred to as a Maclaurin’s series.
, TAYLR0, and SERIES
YLR0, and SERIES are used to generate Taylor 
as Taylor series with residuals. These functions are 
LC/LIMITS&SERIES menu described earlier in this 
rforms a Maclaurin series expansion, i.e., about X = 
n the default independent variable, VX (typically ‘X’). 
 a 4-th order relative power, i.e., the difference 
nd lowest power in the expansion is 4. For example,
 
ces a Taylor series expansion of a function of any 
oint x = a for the order k specified by the user. Thus, 
rmat TAYLR(f(x-a),x,k). For example, 
 
uces a Taylor polynomial using as arguments the 
xpanded, a variable name alone (for Maclaurin’s 
series) or an expression of the form ‘variable = value’ indicating the point 
of expansion of a Taylor series, and the order of the series to be produced. 
Function SERIES returns two output items: a list with four items, and an 
expression for h = x - a, if the second argument in the function call is ‘x=a’, 
i.e., an expression for the increment h. The list returned as the first output 
object includes the following items:
1. Bi-directional limit of the function at point of expansion, i.e., 
2. An equivalent valu
3. Expression for the
4. Order of the resid
Because of the relativ
handle in RPN mode
RPN stack before and
The keystrokes that ge
~
S~!s
Reference
Additional definition
presented in Chapter
)(lim xf
SG49A.book Page 6 Friday, September 16, 2005 1:31 PM
Page 11-6
e of the function near x = a
 Taylor polynomial
ual or remainder
ely large amount of output, this function is easier to 
. For example, the following screen shots show the 
 after using the TAYLR function, as illustrated above:
 
 
 
nerate this particular example are:
!s`!ì2/-
`6!Ö˜$OK$ ˜˜˜˜$OK$ 
s and applications of calculus operations are 
 13 in the calculator’s user’s guide.
ax→
Page 12-1
Chapter 12
Multi-variate Calculus Applications
Multi-variate calculus refers to functions of two or more variables. In this 
Chapter we discuss basic concepts of multi-variate calculus: partial 
derivatives and multiple integrals.
Partial deriva
To quickly calculate 
rules of ordinary der
considering all other 
You can use the der
described in detail 
derivatives (DERVX us
examples of first-orde
used in the first two
(x2+y2)1/2sin(z).
( cos(x
x∂
∂
SG49A.book Page 1 Friday, September 16, 2005 1:31 PM
tives
partial derivatives of multi-variate functions, use the 
ivatives with respect to the variable of interest, while 
variables as constant. For example,
,
ivative functions in the calculator: DERVX, DERIV, ∂, 
in Chapter 11 of this manual, to calculate partial 
es the CAS default variable VX, typically, ‘X’). Some 
r partial derivatives are shown next. The functions 
 examples are f(x,y) = x cos(y), and g(x,y,z) = 
 
 
) ( ) )sin()cos(),cos() yxyx
y
yy −=
∂
∂
=
To define the functions f(x,y) and g(x,y,z), in ALG mode, use: 
DEF(f(x,y)=x*COS(y)) ` DEF(g(x,y,z)=√(x^2+y^2)*SIN(z) `
To type the derivative symbol use ‚¿. The derivative , 
for example, will be entered as ∂x(f(x,y)) ` in ALG mode in the screen.
Multiple integ
A physical interpreta
region R on the x-y p
the surface f(x,y) abo
= {a<x<b, f(x)<y<g(x
integral can be writte
Calculating a doubl
double integral can 
Chapter 2 in the use
calculated directly in 
and using function @EV
Reference
For additional deta
applications see Cha
)),(( yxf
x∂
∂
∫∫φ
R
dA)y,x(
SG49A.book Page 2 Friday, September 16, 2005 1:31 PM
Page 12-2
rals
tion of the double integral of a function f(x,y) over a 
lane is the volume of the solid body contained under 
ve the region R. The region R can be described as R 
)} or as R = {c<y<d, r(y)<x<s(y)}. Thus, the double 
n as
e integral in the calculator is straightforward. A 
be built in the Equation Writer (see example in 
r’s guide), as shown below. This double integral is 
the Equation Writer by selecting the entire expression 
AL. The result is 3/2.
 
ils of multi-variate calculus operations and their 
pter 14 in the calculator’s user’s guide.
∫ ∫∫ ∫ φ=φ= dc
)y(s
)y(r
b
a
)x(g
)x(f
dydx)y,x(dydx)y,x(
Page 13-1
Chapter 13
Vector Analysis Applications
This chapter describes the use of functions HESS, DIV, and CURL, for 
calculating operations of vector analysis.
The del operator
The following operat
vector-based operato
When applied to a 
function, and when 
divergence and the c
divergence produces 
Gradient
The gradient of a sc
. Fun
function.. The functio
φ(x1, x2, …,xn), and 
returns the Hessian 
gradient of the functio
∂φ/∂x2 … ∂φ/∂xn], a
is easier to visualize
function φ(X,Y,Z) = X2
field in the following 
Thus, the gradient is [
Alternatively, use func
[∇
φφ ∇=grad
SG49A.book Page 1 Friday, September 16, 2005 1:31 PM
or, referred to as the ‘del’ or ‘nabla’ operator, is a 
r that can be applied to a scalar or vector function:
scalar function we can obtain the gradient of the 
applied to a vector function we can obtain the 
url of that function. A combination of gradient and 
the Laplacian of a scalar function.
alar function φ(x,y,z) is a vector function defined by 
ction HESS can be used to obtain the gradient of a 
n takes as input a function of n independent variables 
a vector of the functions [‘x1’ ‘x2’…’xn’]. The function 
matrix of the function, H = [hij] = [∂φ/∂xi∂xj], the 
n with respect to the n-variables, grad f = [ ∂φ/∂x1 
nd the list of variables [‘x1’, ‘x2’,…,’xn’]. This function 
 in the RPN mode. Consider as an example the 
 + XY + XZ, we’ll apply function HESS to this scalar 
example:
 
2X+Y+Z, X, X].
tion DERIV as follows:
] [ ] [ ] [ ]
z
k
y
j
x
i
∂
∂
⋅+
∂
∂
⋅+
∂
∂
⋅=
Divergence
The divergence of 
+h(x,y,z)k, is defined
the function, i.e., 
the divergence of 
[XY,X2+Y2+Z2,YZ], th
DIV([X*Y,X^2+Y^2+Z
Curl
The curl of a vector f
by a “cross-product”
. Th
CURL. For example, 
is calculated as follow
Reference
For additional inform
in the calculator’s use
div
FF ×∇=curl
SG49A.book Page 2 Friday, September 16, 2005 1:31 PM
Page 13-2
a vector function, F(x,y,z) = f(x,y,z)i + g(x,y,z)j 
 by taking a “dot-product” of the del operator with 
. Function DIV can be used to calculate 
a vector field. For example, for F(X,Y,Z) = 
e divergence is calculated, in ALG mode, as follows: 
^2,Y*Z],[X,Y,Z])
ield F(x,y,z) = f(x,y,z)i+g(x,y,z)j+h(x,y,z)k,is defined 
 of the del operator with the vector field, i.e., 
e curl of vector field can be calculated with function 
for the function F(X,Y,Z) = [XY,X2+Y2+Z2,YZ], the curl 
s: CURL([X*Y,X^2+Y^2+Z^2,Y*Z],[X,Y,Z])
ation on vector analysis applications see Chapter 15 
r’s guide.
FF •∇=
Page 14-1
Chapter 14
Differential Equations 
In this Chapter we present examples of solving ordinary differential 
equations (ODE) using calculator functions. A differential equation is an 
equation involving derivatives of the independent variable. In most cases, 
we seek the dependent function that satisfies the differential equation.
The CALC/DIF
The DIFFERENTIAL E
provides functions fo
listed below with syst
These functions are b
detail in later parts o
Solution to lin
An equation in wh
derivatives are of th
equation. Otherwise
Function LDEC
The calculator prov
Command) to find th
constantcoefficients,
requires you to provid
DESOLVE: Diffe
when
ILAP: Inver
LAP: LAPla
LDEC: Linea
SG49A.book Page 1 Friday, September 16, 2005 1:31 PM
F menu
QNS.. sub-menu within the CALC („Ö) menu 
r the solution of differential equations. The menu is 
em flag 117 set to CHOOSE boxes:
 
riefly described next. They will be described in more 
f this Chapter.
ear and non-linear equations
ich the dependent variable and all its pertinent 
e first degree is referred to as a linear differential 
, the equation is said to be non-linear.
ides function LDEC (Linear Differential Equation 
e general solution to a linear ODE of any order with 
 whether it is homogeneous or not. This function 
e two pieces of input:
rential Equation SOLVEr, solves differential equations, 
 possible
se LAPlace transform, L-1[F(s)] = f(t)
ce transform, L[f(t)]=F(s)
r Differential Equation Command
• the right-hand side of the ODE
• the characteristic equation of the ODE 
Both of these inputs must be given in terms of the default independent 
variable for the calculator’s CAS (typically X). The output from the function 
is the general solution of the ODE. The examples below are shown in the 
RPN mode:
Example 1 – To solve the homogeneous ODE 
d3y/d
Enter:
0 ` 'X^
The solution is (figure
where cC0, cC1, an
equivalent to
Example 2 – Using th
d3y/d
Enter:
'X^2' ` '
The solution is:
which is equivalent to
y = K1⋅e
–3x + K
 
 
Ch14_DifferentialEquationsQS.fm Page 2 Friday, March 17, 2006 6:23 PM
Page 14-2
x3-4⋅(d2y/dx2) -11⋅(dy/dx)+30⋅y = 0.
3-4*X^2-11*X+30'` LDEC µ
 put together from EQW screenshots):
d cC2 are constants of integration. This result is 
y = K1⋅e
–3x + K2⋅e
5x + K3⋅e
2x.
e function LDEC, solve the non-homogeneous ODE:
x3-4⋅(d2y/dx2)-11⋅(dy/dx)+30⋅y = x2.
X^3-4*X^2-11*X+30'` LDEC µ
2⋅e
5x + K3⋅e
2x + (450⋅x2+330⋅x+241)/13500.
Page 14-3
Function DESOLVE
The calculator provides function DESOLVE (Differential Equation SOLVEr) to 
solve certain types of differential equations. The function requires as input 
the differential equation and the unknown function, and returns the solution 
to the equation if available. You can also provide a vector containing the 
differential equation and the initial conditions, instead of only a differential 
equation, as input to DESOLVE. The function DESOLVE is available in the 
CALC/DIFF menu. E
using RPN mode.
Example 1 – Solve th
In the calculator use:
'd1y(x)+x^
The solution provided
{‘y(x) = (5*INT(EXP(x
, which simplifies to 
The variable OD
You will notice in the
(ODETYPE). This var
and holds a string sh
Press @ODETY to obtain
Example 2 – Solving 
with initial conditions
In the calculator, use:
[‘d1d1y(t)+5*y(t) 
Notice that the initial
‘y(0) = 6/5’, rather 
5)(xy =
SG49A.book Page 3 Friday, September 16, 2005 1:31 PM
xamples of DESOLVE applications are shown below 
e first-order ODE: 
dy/dx + x2⋅y(x) = 5.
2*y(x)=5' ` 'y(x)' ` DESOLVE
 is 
t^3/3),xt,x)+cC0)*1/EXP(x^3/3)}’ } 
ETYPE
 soft-menu key labels a new variable called @ODETY
iable is produced with the call to the DESOL function 
owing the type of ODE used as input for DESOLVE. 
 the string “1st order linear”.
an equation with initial conditions. Solve 
d2y/dt2 + 5y = 2 cos(t/2),
 
y(0) = 1.2, y’(0) = -0.5.
= 2*COS(t/2)’ ‘y(0) = 6/5’ ‘d1y(0) = -1/2’] ` 
‘y(t)’ `
DESOLVE 
 conditions were changed to their Exact expressions, 
than ‘y(0)=1.2’, and ‘d1y(0) = -1/2’, rather than, 
( ).)3/exp()3/exp( 033 Cdxxx +⋅⋅−⋅ ∫
‘d1y(0) = -0.5’. Changing to these Exact expressions facilitates the 
solution.
Press µµ to simplify the result. Use ˜ @EDIT to see this result:
i.e.,
‘y(t) = -((19*√5*S
Press ``J@OD
the ODE type in this c
Laplace Trans
The Laplace transfor
image domain that 
differential equation 
involved in this applic
1. Use of the Laplace
an algebraic equa
2. The unknown F(s) 
manipulation.
3. An inverse Laplace
found in step 2 int
Laplace transfo
The calculator provide
transform and the in
f(VX), where VX is the
calculator returns the 
functions LAP and IL
examples are worked
mode is straightforwa
Example 1 – You ca
following: ‘f(X)’`
The calculator returns
NOTE: To obtain fractional expressions for decimal values use function 
�Q (See Chapter 5).
SG49A.book Page 4 Friday, September 16, 2005 1:31 PM
Page 14-4
IN(√5*t)-(148*COS(√5*t)+80*COS(t/2)))/190)’.
ETY to get the string “Linear w/ cst coeff” for 
ase.
forms
m of a function f(t) produces a function F(s) in the 
can be utilized to find the solution of a linear 
involving f(t) through algebraic methods. The steps 
ation are three:
 transform converts the linear ODE involving f(t) into 
tion.
is solved for in the image domain through algebraic 
 transform is used to convert the image function 
o the solution to the differential equation f(t).
rm and inverses in the calculator
s the functions LAP and ILAP to calculate the Laplace 
verse Laplace transform, respectively, of a function 
 CAS default independent variable (typically X). The 
transform or inverse transform as a function of X. The 
AP are available under the CALC/DIFF menu. The 
 out in the RPN mode, but translating them to ALG 
rd.
n get the definition of the Laplace transform use the 
LAP in RPN mode, or LAP(F(X))in ALG mode. 
 the result (RPN, left; ALG, right):
Page 14-5
 
Compare these expressions with the one given earlier in the definition of 
the Laplace transform
and you will notice th
screen replaces the v
function LAP you get b
f(X).
Example 2 – Determi
The calculator returns
 x⋅e-x.
Fourier series
A complex Fourier se
where
Function FOURI
Function FOURIER pr
Fourier series given 
FOURIER requires yo
function into the CAS
function FOURIER is 
menu („Ö).
L
∫ ⋅=
T
n
tf
T
c
0
ex)(
1
SG49A.book Page 5 Friday, September 16, 2005 1:31 PM
, i.e., 
at the CAS default variable X in the equation writer 
ariable s in this definition. Therefore, when using the 
ack a function of X, which is the Laplace transform of 
ne the inverse Laplace transform of F(s) = sin(s). Use:
‘1/(X+1)^2’`ILAP
 the result: ‘X⋅e-X’, meaning that L -1{1/(s+1)2} = 
ries is defined by the following expression
ER
ovides the coefficient cn of the complex-form of the 
the function f(t) and the value of n. The function 
u to store the value of the period (T) of a T-periodic 
 variable PERIOD before calling the function. The 
available in the DERIV sub-menu within the CALC 
{ } ∫ ∞ −⋅==
0
,)()()( dtetfsFtf st
∑
+∞
−∞=
⋅=
n
n
T
tin
ctf ),
2
exp()(
π
∞−−−∞=⋅⋅
⋅⋅⋅
ndtt
T
ni
.,...2,1,0,1,2,...,,)
2
p(
π
Fourier series for a quadratic function
Determine the coefficients c0, c1, and c2 for the function g(t) = (t-1)
2+(t-1), 
with period T = 2.
Using the calculator in ALG mode, first we define functions f(t) and g(t):
Next, we move to th
value of variable PER
„(hold) §
Return to the sub-dir
calculate the coeffici
before trying the exe
menu (‚×).
SG49A.book Page 6 Friday, September 16, 2005 1:31 PM
Page 14-6
e CASDIR sub-directory under HOME to change the 
IOD, e.g.,
`J@)CASDI`2K@PERIOD `
ectory where you defined functions f and g, and 
ents. Set CAS to Complex mode (see chapter 2) 
rcises. Function COLLECT is available in the ALG 
 
 
Page 14-7
 
Thus, c0 = 1/3, c1 = (π⋅i+2)/π
2, c2 = (π⋅i+1)/(2π
2).
The Fourier series with
g(t) ≈ Re[(1/3) +
Reference
For additional defi
differential equations
transforms, as well a
in the calculator’s use
SG49A.book Page 7 Friday, September 16, 2005 1:31 PM
 three elements will be written as
 (π⋅i+2)/π2⋅exp(i⋅π⋅t)+(π⋅i+1)/(2π2)⋅exp(2⋅i⋅π⋅t)].
nitions, applications, and exercises on solving 
, using Laplace transform, and Fourier series and 
s numerical and graphical methods, see Chapter 16 
r’s guide.
SG49A.book Page 8 Friday, September 16, 2005 1:31 PM
Page 15-1
Chapter 15
Probability Distributions
In this Chapter we provide examples of applications of the pre-defined 
probability distributions in the calculator.
The MTH/PROBABILITY.. sub-menu - part 1
The MTH/PROBABIL
sequence „´. 
following functions ar
In this section we disc
Factorials, com
The factorial of an in
definition, 0! = 1.
Factorials are used in
combinations of obje
objects from a set of 
Also, the number of c
We can calculate com
COMB, PERM, and
operation of those fun
• COMB(n,r): Calcu
a time
rn
P =
n
r
n
=⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
SG49A.book Page 1 Friday, September 16, 2005 1:31 PM
ITY.. sub-menu is accessible through the keystroke 
 With system flag 117 set to CHOOSE boxes, the 
e available in the PROBABILITY.. menu:
 
uss functions COMB, PERM, ! (factorial), and RAND.
binations, and permutations
teger n is defined as: n! = n⋅ (n-1) ⋅ (n-2)…3⋅2⋅1. By 
 the calculation of the number of permutations and 
cts. For example, the number of permutations of r 
n distinct objects is 
ombinations of n objects taken r at a time is
binations, permutations, and factorials with functions 
 ! from the MTH/PROBABILITY.. sub-menu. The 
ctions is described next:
lates the number of combinations of n items taken r at 
)!/(!)1)...(1)(1( rnnrnnnn −=+−−−
)!(!
!
!
)1)...(2)(1(
rnr
n
r
rnnn
−
=
+−−−
• PERM(n,r): Calculates the number of permutations of n items taken r at 
a time
• n!: Factorial of a positive integer. For a non-integer, x! returns Γ(x+1), 
where Γ(x) is the Gamma function (see Chapter 3). The factorial 
symbol (!) can be entered also as the keystroke combination 
~‚2.
Example of applications of these functions are shown next:
Random numbe
The calculator provi
uniformly distributed 
a random number, u
menu. The followi
produced using RAN
differ from these).
Additional details on
Chapter 17 of the use
start lists of random 
user’s guide.
SG49A.book Page 2 Friday, September 16, 2005 1:31 PM
Page 15-2
rs
des a random number generator that returns a 
random real number between 0 and 1. To generate 
se function RAND from the MTH/PROBABILITY sub-
ng screen shows a number of random numbers 
D. (Note: The random numbers in your calculator will 
 random numbers in the calculator are provided in 
r’s guide. Specifically, the use of function RDZ, to re-
numbers is presented in detail in Chapter 17 of the 
Page 15-3
The MTH/PROB menu - part 2
In this section we discuss four continuous probability distributions that are 
commonly used for problems related to statistical inference: the normal 
distribution, the Student’s t distribution, the Chi-square (χ2) distribution, and 
the F-distribution. The functions provided by the calculator to evaluate 
probabilities for these distributions are NDIST, UTPN, UTPT, UTPC, and 
UTPF. These function
introduced earlier in 
menu: „´ and 
The Normal dis
Functions NDIST and 
and variance σ2.
To calculate the value
the normal distributio
that for a normal dis
function is useful to p
The calculator also p
normal distribution, i.
represents a probabil
with µ = 1.0, σ2 = 0.
The Student-t d
The Student-t, or simp
the degrees of freed
values of the uppe
distribution, function 
UTPT(ν,t) = P(T>t) = 1
SG49A.book Page 3 Friday, September 16, 2005 1:31 PM
s are contained in the MTH/PROBABILITY menu 
this chapter. To see these functions activate the MTH 
select the PROBABILITY option:
 
tribution
UTPN relate to the Normal distribution with mean µ , 
 of probability density function, or pdf, of the f(x) for 
n, use function NDIST(µ, σ2, x). For example, check 
tribution, NDIST(1.0, 0.5, 2.0) = 0.20755374. This 
lot the Normal distribution pdf. 
rovides function UTPN that calculates the upper-tail 
e., UTPN(µ, σ2, x) = P(X>x) = 1 - P(X<x), where P() 
ity. For example, check that for a normal distribution, 
5, UTPN(1.0, 0.5, 0.75) = 0.638163.
istribution
ly, the t-, distribution has one parameter ν, known as 
om of the distribution. The calculator provides for 
r-tail (cumulative) distribution function for the t-
UTPT, given the parameter ν and the value of t, i.e., 
-P(T<t). For example, UTPT(5,2.5) = 2.7245…E-2. 
The Chi-square distribution
The Chi-square (χ2) distribution has one parameter ν, known as the 
degrees of freedom. The calculator provides for values of the upper-tail 
(cumulative) distribution function for the χ2-distribution using UTPC given 
the value of x and the parameter ν. The definition of this function is, 
therefore, UTPC(ν,x) = P(X>x) = 1 - P(X<x). For example, UTPC(5, 2.5) = 
0.776495…
The F distributio
The F distribution has
and νD = denomina
values of the uppe
distribution, function U
of F. The definition o
1 - P(ℑ<F). For exam
Reference
For additional proba
to Chapter 17 in the 
SG49A.book Page 4 Friday, September 16, 2005 1:31 PM
Page 15-4
n
 two parameters νN = numerator degrees of freedom, 
tor degrees of freedom. The calculator provides for 
r-tail (cumulative) distribution function for the F 
TPF, given the parameters νN and νD, and the value 
f this function is, therefore, UTPF(νN,νD,F) = P(ℑ>F) = 
ple, to calculate UTPF(10,5, 2.5) = 0.1618347…
bility distributions and probability applications, refer 
calculator’s user’s guide.
Page 16-1
Chapter 16
Statistical Applications
The calculator provides the following pre-programmed statistical features 
accessible through the keystroke combination ‚Ù (the 5 key):
Entering data
Applications numbere
be available as col
accomplished is by e
„², and then u
For example, enter 
Chapters 8 or 9 in th
2.1 1.2 3.1 4
The screen may look 
Notice the variable @£
A simpler way to ent
(such as Single-v
first screenshot above
Enter the data as bef
data you have entere
SG49A.book Page 1 Friday, September 16, 2005 1:31 PM
d 1, 2, and 4 in the list above require that the data 
umns of the matrix ΣDAT. One way this can be 
ntering the data in columns using the Matrix Writer, 
sing function STOΣ to store the matrix into ΣDAT.
the following data using the Matrix Writer (see 
is guide), and store the data into ΣDAT:
.5 2.3 1.1 2.3 1.5 1.6 2.2 1.2 2.5.
like this:
 
DAT listed in the soft menu keys.
er statistical data is to launch a statistics application 
ar, Frequencies or Summary stats, see 
) and press #EDIT#. This launches the Matrix Writer. 
ore. In this case, when you exit the Matrix Writer, the 
d is automatically saved in ΣDAT.
Calculating single-variable statistics
After entering the column vector into ΣDAT, press ‚Ù @@@OK@@ to select 
1. Single-var.. The following input form will be provided:
The form lists the dat
only one column in th
keys, and press the 
Standard Deviation, V
Minimum values) tha
press @@@OK@@. The selec
screen of your calcula
Sample vs. po
The pre-programmed
be applied to a finite
the SINGLE-VARIAB
the values of the var
using n in the deno
example above, use 
Type: and re-calculate
SG49A.book Page 2 Friday, September 16, 2005 1:31 PM
Page 16-2
a in ΣDAT, shows that column 1 is selected (there is 
e current ΣDAT). Move about the form with the arrow 
 soft menu key to select those measures (Mean, 
ariance, Total number of data points, Maximum and 
t you want as output of this program. When ready, 
ted values will be listed, appropriately labeled, in the 
tor. For example:
 
pulation
 functions for single-variable statistics used above can 
 population by selecting the Type:Population in 
LE STATISTICS screen. The main difference is in 
iance and standard deviation which are calculated 
minator of the variance, rather than (n-1). For the 
now the @CHOOS soft menu key to select population as 
 measures:
Page 16-3
 
Obtaining fre
The application 2. 
obtain frequency dist
in the form of a colu
press ‚Ù˜@@@O
fields:
Given a set of n data
one can group the da
frequency or numbe
application 2. Fre
frequency count, and
minimum and above 
As an example, gen
using the command 
ΣDAT: the m
Col: the c
X-Min: the m
distri
Bin Count: the n
(defa
Bin Width: the u
distri
SG49A.book Page 3 Friday, September 16, 2005 1:31 PM
quency distributions
Frequencies.. in the STAT menu can be used to 
ributions for a set of data. The data must be present 
mn vector stored in variable ΣDAT. To get started, 
K@@@. The resulting input form contains the following 
 values: {x1, x2, …, xn} listed in no particular order, 
ta into a number of classes, or bins by counting the 
r of values corresponding to each class. The 
quencies.. in the STAT menu will perform this 
 will keep track of those values that may be below the 
the maximum class boundaries (i.e., the outliers).
erate a relatively large data set, say 200 points, by 
RANM({200,1}), and storing the result into variable 
atrix containing the data of interest.
olumn of ΣDAT that is under scrutiny.
inimum class boundary to be used in the frequency 
bution (default = -6.5).
umber of classes used in the frequency distribution 
ult = 13).
niform width of each class in the frequency 
bution (default = 1).
ΣDAT, by using function STOΣ (see example above). Next, obtain single-
variable information using: ‚Ù @@@OK@@@. The results are:
This information indicates that our data ranges from -9 to 9. To produce a 
frequency distribution
of width 2 each.
• Select the program
The data is alread
value 1 since we h
• Change X-Min to 
@@@OK@@@.
Using the RPN mode,
in stack level 2, and a
vector in stack level 1
the frequency count w
indicating that there a
8 larger than 8.
• Press ƒ to drop
result is the freque
The bins for this frequ
and 6 to 8, i.e., 8 of 
stack, namely (for this
This means that there
4,-2], 17 in [-2,0], 26
You can also check th
show above, you wi
namely, 200.
SG49A.book Page 4 Friday, September 16, 2005 1:31 PM
Page 16-4
 we will use the interval (-8, 8) dividing it into 8 bins 
 2. Frequencies.. by using ‚Ù˜ @@@OK@@@. 
y loaded in ΣDAT, and the option Col should hold the 
ave only one column in ΣDAT.
-8, Bin Count to 8, and Bin Width to 2, then press 
 the results are shown in the stack as a column vector 
 row vector of two components in stack level 1. The 
 is the number of outliers outside of the interval where 
as performed. For this case, I get the values [14. 8.] 
re, in the ΣDAT vector, 14 values smaller than -8 and 
 the vector of outliers from the stack. The remaining 
ncy count of data.
ency distribution will be: -8 to -6, -6 to -4, …, 4 to 6, 
them, with the frequencies in the column vector in the 
 case):
23, 22, 22, 17, 26, 15, 20, 33.
 are 23 values in the bin [-8,-6], 22 in [-6,-4], 22 in [-
 in [0,2], 15 in [2,4], 20 in [4,6], and 33 in [6,8]. 
at adding all these values plus the outliers, 14 and 8, 
ll get the total number of elements in the sample, 
Page 16-5
Fitting data to a function y = f(x)
The program 3. Fit data.., available as option number 3 in the STAT 
menu, can be used to fit linear, logarithmic, exponential, and power 
functions to data sets (x, y), stored in columns of the ΣDAT matrix. For this 
application, you need to have at least two columns in your ΣDAT variable.
For example, to fit a linear relationship to the data shown in the table 
below:
• First, enter the two
Matrix Writer, and
• To access the prog
‚Ù˜˜@
already loaded. I
parameters for a l
• To obtain the data
shown below for o
lines in RPN mode
3: 
2: 
1: 
SG49A.book Page 5 Friday, September 16, 2005 1:31 PM
 columns of data into variable ΣDAT by using the 
 function STOΣ.
ram 3. Fit data.., use the following keystrokes: 
@@OK@@@. The input form will show the current ΣDAT, 
f needed, change your set up screen to the following 
inear fitting:
 fitting press @@OK@@. The output from this program, 
ur particular data set, consists of the following three 
:
'0.195238095238 + 2.00857242857*X'
Correlation: 0.983781424465
Covariance: 7.03
x y
0 0.5
1 2.3
2 3.6
3 6.7
4 7.2
5 11
Level 3 shows the form of the equation. Level 2 shows the sample 
correlation coefficient, and level 1 shows the covariance of x-y. For 
definitions of these parameters see Chapter 18 in the user’s guide.
For additional information on the data-fit feature of the calculator see 
Chapter 18 in the user’s guide.
Obtaining additional summary statistics
The application 4. S
some calculations for
more, move to the fou
@@@OK@@@. The resulting i
Many of these summ
variables (x, y) that m
program can be thou
As an example, for th
statistics.
• To access the sum
‚Ù˜˜˜
• Select the column 
X-Col: 1, and Y-Co
• Using the k
etc.
ΣDAT: the m
X-Col, Y-Col: these
colum
colum
one 
have
_ΣX _ ΣY…: summ
prog
when
SG49A.book Page 6 Friday, September 16, 2005 1:31 PM
Page 16-6
ummary stats.. in the STAT menu can be useful in 
 sample statistics. To get started, press ‚Ù once 
rth option using the down-arrow key ˜, and press 
nput form contains the following fields:
ary statistics are used to calculate statistics of two 
ay be related by a function y = f(x). Therefore, this 
ght off as a companion to program 3. Fit data..
e x-y data currently in ΣDAT, obtain all the summary 
mary stats… option, use: 
@@@OK@@@
numbers corresponding to the x- and y-data, i.e., 
l: 2.
ey select all the options for outputs, i.e., _ΣX, _ΣY, 
atrix containing the data of interest.
 options apply only when you have more than two 
ns in the matrix ΣDAT. By default, the x column is 
n 1, and the y column is column 2. If you have only 
column, then the only setting that makes sense is to 
 X-Col: 1.
ary statistics that you can choose as results of this 
ram by checking the appropriate field using 
 that field is selected.
Page 16-7
• Press @@@OK@@@ to obta
Confidence in
The application 6.
‚Ù—@@@OK@@@. T
These options are to b
1. Z-INT: 1 µ.: Single
µ, with known pop
population varian
2. Z-INT: µ1−µ2.: Co
means, µ1- µ2, wi
samples with unkn
3. Z-INT: 1 p.: Single
large samples with
SG49A.book Page 7 Friday, September 16, 2005 1:31 PM
in the following results:
tervals
 Conf Interval can be accessed by using 
he application offers the following options:
e interpreted as follows:
 sample confidence interval for the population mean, 
ulation variance, or for large samples with unknown 
ce.
nfidence interval for the difference of the population 
th either known population variances, or for large 
own population variances.
 sample confidence interval for the proportion, p, for 
 unknown population variance.
4. Z-INT: p1− p2.: Confidence interval for the difference of two 
proportions, p1-p2, for large samples with unknown population 
variances.
5. T-INT: 1 µ.: Single sample confidence interval for the population mean, 
µ, for small samples with unknown population variance.
6. T-INT: µ1−µ2.: Confidence interval for the difference of the population 
means, µ1- µ2, for small samples with unknown population variances.
Example 1 – Determi
population if a samp
sample is ⎯x = 23.3, 
α = 0.05. The confid
Select case 1 from th
values required in the
Press @HELP to obtain 
interval in terms of ra
down the resulting sc
done with the help sc
To calculate the conf
calculator is:
Press @GRAPHto see
information:
SG49A.book Page 8 Friday, September 16, 2005 1:31 PM
Page 16-8
ne the centered confidence interval for the mean of a 
le of 60 elements indicate that the mean value of the 
and its standard deviation is s = 5.2. Use 
ence level is C = 1-α = 0.95. 
e menu shown above by pressing @@@OK@@@. Enter the 
 input form as shown:
a screen explaining the meaning of the confidence 
ndom numbers generated by a calculator. To scroll 
reen use the down-arrow key ˜. Press @@@OK@@@ when 
reen. This will return you to the screen shown above.
idence interval, press @@@OK@@@. The result shown in the 
 a graphical display of the confidence interval 
Page 16-9
The graph shows the
function), the locatio
and the correspondin
@TEXT to return to the 
confidence interval en
display.
Additional examples 
Chapter 18 in the ca
Hypothesis te
A hypothesis is a dec
respect to its mean). 
test on a sample tak
decision-making are c
The calculator provid
Hypoth. tests.. can be
As with the calcula
program offers the fo
These options are inte
1. Z-Test: 1 µ.: Singl
µ, with known pop
population varian
SG49A.book Page 9 Friday, September 16, 2005 1:31 PM
 standard normal distribution pdf (probability density 
n of the critical points ±zα/2, the mean value (23.3) 
g interval limits (21.98424 and 24.61576). Press 
previous results screen, and/or press @@@OK@@@ to exit the 
vironment. The results will be listed in the calculator’s 
of confidence interval calculations are presented in 
lculator’s user’s guide.
sting
laration made about a population (for instance, with 
Acceptance of the hypothesis is based on a statistical 
en from the population. The consequent action and 
alled hypothesis testing.
es hypothesis testing procedures under application 5. 
 accessed by using ‚Ù——@@@OK@@@.
tion of confidence intervals, discussed earlier, this 
llowing 6 options:
rpreted as in the confidence interval applications:
e sample hypothesis testing for the population mean, 
ulation variance, or for large samples with unknown 
ce.
2. Z-Test: µ1−µ2.: Hypothesis testing for the difference of the population 
means, µ1- µ2, with either known population variances, or for large 
samples with unknown population variances.
3. Z-Test: 1 p.: Single sample hypothesis testing for the proportion, p, for 
large samples with unknown population variance.
4. Z-Test: p1− p2.: Hypothesis testing for the difference of two proportions, 
p1-p2, for large samples with unknown population variances.
5. T-Test: 1 µ.: Singl
µ, for small sampl
6. T-Test: µ1−µ2.: Hyp
means, µ1- µ2, for
Example 1 – For µ0 =
the hypothesis H0: µ 
Press ‚Ù——
calculator. Press @@@OK
Enter the following da
You are then asked to
Select µ ≠ 150. Then
SG49A.book Page 10 Friday, September 16, 2005 1:31 PM
Page 16-10
e sample hypothesis testing for the population mean, 
es with unknown population variance.
othesis testing for the difference of the population 
 small samples with unknown population variances.
 150, σ = 10, ⎯x = 158, n = 50, for α = 0.05, test 
= µ0, against the alternative hypothesis, H1: µ ≠ µ0.
@@@OK@@@ to access the confidence interval feature in the 
@@@ to select option 1. Z-Test: 1 µ.
ta and press @@@OK@@@:
 select the alternative hypothesis:
, press @@@OK@@@. The result is:
Page 16-11
Then, we reject H0: µ
z0 = 5.656854. The
±zα/2 = ±1.959964,
This information can b
@GRAPH:
Reference
Additional materials
concepts, and advan
18 in the user’s guide
SG49A.book Page 11 Friday, September 16, 2005 1:31 PM
 = 150, against H1: µ ≠ 150. The test z value is 
 P-value is 1.54×10-8. The critical values of 
 corresponding to critical ⎯x range of {147.2 152.8}.
e observed graphically by pressing the soft-menu key 
 on statistical analysis, including definitions of 
ced statistical applications, are available in Chapter 
.
SG49A.book Page 12 Friday, September 16, 2005 1:31 PM
Page 17-1
Chapter 17
Numbers in Different Bases
Besides our decimal (base 10, digits = 0-9) number system, you can work 
with a binary system (base 2, digits = 0,1), an octal system (base 8, digits 
= 0-7), or a hexadecimal system (base 16, digits=0-9,A-F), among others. 
The same way that the decimal integer 321 means 3x102+2x101+1x100, 
the number 100110,
1x25 + 0x24 + 0x2
The BASE men
The BASE menu is ac
flag 117 set to CH
following entries are 
 
With system flag 11
following:
This figure shows tha
menu are themselves
Chapter 19 of the ca
SG49A.book Page 1 Friday, September 16, 2005 1:31 PM
 in binary notation, means 
3 + 1x22 + 1x21 + 0x20 = 32+0+0+4+2+0 = 38.
u
cessible through ‚ã(the 3 key). With system 
OOSE boxes (see Chapter 1 in this guide), the 
available: 
 
7 set to SOFT menus, the BASE menu shows the 
 
t the LOGIC, BIT, and BYTE entries within the BASE 
 sub-menus. These menus are discussed in detail in 
lculator’s user’s guide.
Writing non-decimal numbers
Numbers in non-decimal systems, referred to as binary integers, are written 
preceded by the # symbol („â) in the calculator. To select the current 
base to be used for binary integers, choose either HEX (adecimal), DEC 
(imal), OCT (al), or BIN (ary) in the BASE menu. For example, if is 
selected, binary integers will be a hexadecimal numbers, e.g., #53, 
#A5B, etc. As different systems are selected, the numbers will be 
automatically convert
To write a number in 
with either h (hexadec
Reference
For additional details
the calculator’s user’s
HEX
OCT
SG49A.book Page 2 Friday, September 16, 2005 1:31 PM
Page 17-2
ed to the new current base.
a particular system, start the number with # and end 
imal), d (decimal), o (octal), or b (binary), examples:
 on numbers from different bases see Chapter 19 in 
 guide.
DEC
BIN
Page 18-1
Chapter 18
Using SD cards
The calculator has a memory card slot into which you can insert an SD 
flash card for backing up calculator objects, or for downloading objects 
from other sources. The SD card in the calculator will appear as port 
number 3.
Inserting and
The SD slot is located
number keys. SD car
label on what would 
holding the HP 50g w
card should face dow
50g. The card will g
and then it will requi
card is almost flush w
visible.
To remove an SD car
edge of the card and
distance, allowing it n
Formatting an
Most SD cards will al
file system that is inco
with cards in the FAT1
You can format an SD
from the calculator (
your calculator has fr
1. Insert the SD card
section).
2. Hold down the ‡
key and then relea
several choices.
3. Press 0 for FORMA
NOTE: formatting 
it.
Ch18_Using SD cardQS.fm Page 1 Friday, February 24, 2006 8:39 PM
 removing an SD card
 on the bottom edge of the calculator, just below the 
ds must be inserted facing down. Most cards have a 
usually be considered the top of the card. If you are 
ith the keyboard facing up, then this side of the SD 
n or away from you when being inserted into the HP 
o into the slot without resistance for most of its length 
re slightly more force to fully insert it. A fully inserted 
ith the case, leaving only the top edge of the card 
d, turn off the HP 50g, press gently on the exposed 
 push in. The card should spring out of the slot a small 
ow to be easily removed from the calculator.
 SD card
ready be formatted, but they may be formatted with a 
mpatible with the HP 50g. The HP 50g will only work 
6 or FAT32 format.
 card from a PC, or from the calculator. If you do it 
using the method described below), make sure that 
esh or fairly new batteries.
 into the card slot (as explained in the previous 
 key and then press the D key. Release the D 
se the ‡ key. The system menu is displayed withT. The formatting process begins.
an SD card deletes all the data that is currently on 
4. When the formatting is finished, the HP 50g displays the message 
"FORMAT FINISHED. PRESS ANY KEY TO EXIT". To exit the system 
menu, hold down the ‡ key, press and release the C key and then 
release the ‡ key.
The SD card is now ready for use. It will have been formatted in FAT32 
format.
Accessing obj
Accessing an object o
in ports 0, 1, or 2. H
are using the LIB func
using the Filer, or File
Tree view will show:
Long names of files on
format in the Filer (tha
three character exten
will be displayed, unl
these cases, its type i
In addition to using Fi
store objects on, and 
Storing object
To store an object, us
• In algebraic mode
Enter object, press
(e.g., :3:VAR1),
• In RPN mode: 
Enter object, type 
:3:VAR1), press
Ch18_Using SD cardQS.fm Page 2 Friday, February 24, 2006 8:39 PM
Page 18-2
ects on an SD card
n the SD card is similar to when an object is located 
owever, port 3 will not appear in the menu when you 
tion (‚á). The SD files can only be managed 
 Manager („¡). When starting the Filer, the 
 an SD card are supported, but are displayed in 8.3 
t is, their names are truncated to 8 characters and a 
sion is added as a suffix). The type of each object 
ess it is a PC object or an object of unknown type. (In 
s listed as String.) 
le Manager operations, you can use STO and RCL to 
recall objects from, the SD card.
s on the SD card
e function STO as follows:
: 
 K, type the name of the stored object using port 3 
 press `.
the name of the stored object using port 3 (e.g., 
 K.
Page 18-3
Note that if the name of the object you intend to store on an SD card is 
longer than eight characters, it will appear in 8.3 DOS format in port 3 in 
the Filer once it is stored on the card.
Recalling an object from the SD card
To recall an object from the SD card onto the screen, use function RCL, as 
follows:
• In algebraic mode
Press „©, ty
:3:VAR1), press
• In RPN mode: 
Type the name of 
press „©.
With the RCL comma
path in the command
path, like in a DOS
specify the position o
variables stored withi
path. In this case, th
recalled, and the ind
Note that in the case
full name of the obje
command.
Purging an ob
To purge an object fr
as follows:
• In algebraic mode
Press I @PURGE, 
:3:VAR1), press
• In RPN mode: 
Type the name of 
press I @PURGE.
Note that in the case
full name of the obje
command.
SG49A.book Page 3 Friday, September 16, 2005 1:31 PM
: 
pe the name of the stored object using port 3 (e.g., 
 `.
the stored object using port 3 (e.g., :3:VAR1), 
nd, it is possible to recall variables by specifying a 
, e.g., in RPN mode: :3: {path}`RCL. The 
 drive, is a series of directory names that together 
f the variable within a directory tree. However, some 
n a backup object cannot be recalled by specifying a 
e full backup object (e.g., a directory) will have to be 
ividual variables then accessed on the screen.
 of objects with long files names, you can specify the 
ct, or its truncated 8.3 name, when issuing an RCL 
ject from the SD card
om the SD card onto the screen, use function PURGE, 
: 
type the name of the stored object using port 3 (e.g., 
 `.
the stored object using port 3 (e.g., :3:VAR1), 
 of objects with long files names, you can specify the 
ct, or its truncated 8.3 name, when issuing a PURGE 
Purging all objects on the SD card (by 
reformatting)
You can purge all objects from the SD card by reformatting it. When an SD 
card is inserted, @FORMA appears an additional menu item in File Manager. 
Selecting this option reformats the entire card, a process which also deletes 
every object on the card.
Specifying a d
You can store, recall,
an SD card. Note th
card, the ³ key 
subdirectory, the nam
using the …Õ ke
For example, suppos
directory called PRO
level of the stack, pre
!ê3
This will store the obj
directory named PRO
You can specify any n
to an object in a third
Note that pressing ~
NOTE: If PROGS 
created.
SG49A.book Page 4 Friday, September 16, 2005 1:31 PM
Page 18-4
irectory on an SD card
 evaluate and purge objects that are in directories on 
at to work with an object at the root level of an SD 
is used. But when working with an object in a 
e containing the directory path must be enclosed 
ys.
e you want to store an object called PROG1 into a 
GS on an SD card. With this object still on the first 
ss: 
™…Õ~~progs…/
prog1`K
ect previously on the stack onto the SD card into the 
GS into an object named PROG1.
umber of nested subdirectories. For example, to refer 
-level subdirectory, your syntax would be:
:3:”DIR1/DIR2/DIR3/NAME”
…/ produces the forward slash character.
does not exist, the directory will be automatically 
Page 19-1
Chapter 19
Equation Library
The Equation Library is a collection of equations and commands that 
enable you to solve simple science and engineering problems. The library 
consists of more than 300 equations grouped into 15 technical subjects 
containing more than 100 problem titles. Each problem title contains one 
or more equations tha
Example: Examine 
NOTE: the exampl
RPN and that flag –
use the numeric solv
Step 1: Fix the disp
Library app
squares, pr
H˜~
G—`
Step 2: Select the M
~m˜
Step 3: Select Pro
describes th
˜˜#PI
SG49A.book Page 1 Friday, September 16, 2005 1:31 PM
t help you solve that type of problem.
the equation set for Projectile Motion. 
es in this chapter assume that the operating mode is 
117 is set. (Flag –117 should be set whenever you 
er to solve equations in the equations library.)
lay to 2 decimal places and then open the Equation 
lication. (If #SI# and #UNIT# aren’t flagged with small 
ess each of the corresponding menu keys once.)
f™2` 
#EQLIB #EQNLI 
otion subject area and open its catalog.
`
jectile Motion and look at the diagram that 
e problem.
C#
Now use this equa
example.
Step 4: View the five equations in the Projectile Motion set. All five are 
used interchangeably in order to solve for missing variables (see 
the next example).
#EQN# #NXEQ# #NXEQ# #NXEQ# #NXEQ#
Step 5: Examine th
#VARS#
and —as
Example:You estima
punt a soc
elevation a
kick it? Ho
could they
velocity, b
(Ignore the
Step 1: Start solvin
#SOLV#
Step 2: Enter the 
correspond
are zero.) 
values. (Yo
initially sho
SG49A.book Page 2 Friday, September 16, 2005 1:31 PM
Page 19-2
tion set to answer the questions in the following 
e variables used by the equation set.
 ˜ needed
te that on average professional goalkeepers can 
cer ball a distance (R) of 65 meters downfield at an 
ngle (0) of 50 degrees. At what velocity (v0) do they 
w high is the ball halfway through its flight? How far 
 drop kick the ball if they used the same kicking 
ut changed the elevation angle to 30 degrees? 
 effects of drag on the ball.)
g the problem.
known values and press the soft menu key 
ing to the variable. (You can assume that x0 and y0
Notice that the menu labels turn black as you store 
u will need to press L to see the variables that are 
wn.)
Page 19-3
0 *!!!!!!X0!!!!!+ 0 *!!!!!!Y0!!!!!+ 50 *!!!!!!Ô0!!!!!+
L65*!!!!!!R!!!!!+
Step 3: Solve for t
! and t
!*!!!!!!V0!!!!!+
Step 4: Recall the 
and enter 
right-shifte
calculator 
to the R o
previous ca
@ ##R#- 
2/L
Step 5: Solve for th
other varia
order to so
! *!!!!!!Y!!!!!+
Step 6: Enter the n
the previou
30 ##¢0#- 
™L *!!!!!!V0!!!
! *!!!!!!!!R!!!!!
SG49A.book Page 3 Friday, September 16, 2005 1:31 PM
he velocity, v0. (You solve for a variable by pressing 
hen the variable’s menu key.)
range, R, divide by 2 to get the halfway distance, 
that as thex-coordinate. Notice that pressing the 
d version of a variable’s menu key causes the 
to recall its value to the stack. (The small square next 
n the menu label indicates that it was used in the 
lculation.)
 
L*!!!!!!X!!!!!+
e height, y. Notice that the calculator finds values for 
bles as needed (shown by the small squares) in 
lve for the specified variable.
ew value for the elevation angle (30 degrees), store 
sly computed initial velocity (v0) and then solve for R.
!!+
!!+
Reference
For additional details on the Equation Library, see Chapter 27 in the 
calculator’s user’s guide.
SG49A.book Page 4 Friday, September 16, 2005 1:31 PM
Page 19-4
Page W-1
Limited Warranty
HP 50g graphing calculator; Warranty period: 12 months 
1. HP warrants to you, the end-user customer, that HP hardware, 
accessories and supplies will be free from defects in materials and 
workmanship after the date of purchase, for the period specified above. 
If HP receives notice of such defects during the warranty period, HP 
will, at its option, 
defective. Replace
2. HP warrants to yo
programming instr
specified above, d
properly installed 
the warranty perio
execute its progra
3. HP does not warra
uninterrupted or er
repair or replace a
entitled to a refund
product with proof
4. HP products may c
performance or m
5. Warranty does no
inadequate mainte
or supplies not sup
(d) operation outsi
the product, or (e)
6. HP MAKES NO O
WHETHER WRITT
LAW, ANY IMPLIE
MERCHANTABILIT
PARTICULAR PURP
EXPRESS WARRAN
provinces do not a
warranty, so the a
This warranty give
other rights that va
to province.
7. TO THE EXTENT A
WARRANTY STAT
WarrantyQS49_E.fm Page 1 Friday, February 24, 2006 8:25 PM
either repair or replace products which prove to be 
ment products may be either new or like-new.
u that HP software will not fail to execute its 
uctions after the date of purchase, for the period 
ue to defects in material and workmanship when 
and used. If HP receives notice of such defects during 
d, HP will replace software media which does not 
mming instructions due to such defects. 
nt that the operation of HP products will be 
ror free. If HP is unable, within a reasonable time, to 
ny product to a condition as warranted, you will be 
 of the purchase price upon prompt return of the 
 of purchase.
ontain remanufactured parts equivalent to new in 
ay have been subject to incidental use.
t apply to defects resulting from (a) improper or 
nance or calibration, (b) software, interfacing, parts 
plied by HP, (c) unauthorized modification or misuse, 
de of the published environmental specifications for 
 improper site preparation or maintenance.
THER EXPRESS WARRANTY OR CONDITION 
EN OR ORAL. TO THE EXTENT ALLOWED BY LOCAL 
D WARRANTY OR CONDITION OF 
Y, SATISFACTORY QUALITY, OR FITNESS FOR A 
OSE IS LIMITED TO THE DURATION OF THE 
TY SET FORTH ABOVE. Some countries, states or 
llow limitations on the duration of an implied 
bove limitation or exclusion might not apply to you. 
s you specific legal rights and you might also have 
ry from country to country, state to state, or province 
LLOWED BY LOCAL LAW, THE REMEDIES IN THIS 
EMENT ARE YOUR SOLE AND EXCLUSIVE 
REMEDIES. EXCEPT AS INDICATED ABOVE, IN NO EVENT WILL HP 
OR ITS SUPPLIERS BE LIABLE FOR LOSS OF DATA OR FOR DIRECT, 
SPECIAL, INCIDENTAL, CONSEQUENTIAL (INCLUDING LOST PROFIT 
OR DATA), OR OTHER DAMAGE, WHETHER BASED IN CONTRACT, 
TORT, OR OTHERWISE. Some countries, States or provinces do not 
allow the exclusion or limitation of incidental or consequential 
damages, so the above limitation or exclusion may not apply to you.
8. The only warrantie
express warranty s
HP shall not be lia
contained herein.
FOR CONSUMER 
ZEALAND: THE WAR
EXCEPT TO THE EX
RESTRICT OR MODIF
STATUTORY RIGHTS 
YOU.
SG49A.book Page 2 Friday, September 16, 2005 1:31 PM
Page W-2
s for HP products and services are set forth in the 
tatements accompanying such products and services. 
ble for technical or editorial errors or omissions 
TRANSACTIONS IN AUSTRALIA AND NEW 
RANTY TERMS CONTAINED IN THIS STATEMENT, 
TENT LAWFULLY PERMITTED, DO NOT EXCLUDE, 
Y AND ARE IN ADDITION TO THE MANDATORY 
APPLICABLE TO THE SALE OF THIS PRODUCT TO 
Page W-3
Service
Europe Country : Telephone numbers 
Austria +43-1-3602771203
Belgium +32-2-7126219
Denmark +45-8-2332844
Eastern Europe countries +420-5-41422523
Finl
Fra
Ge
Gre
Ho
Ital
No
Por
Spa
Sw
Sw
Turk
UK
Cze
Sou
Lux
Oth
Asia Pacific Co
Aus
Sin
SG49A.book Page 3 Friday, September 16, 2005 1:31 PM
and +358-9-640009
nce +33-1-49939006
rmany +49-69-95307103
ece +420-5-41422523
lland +31-2-06545301
y +39-02-75419782
rway +47-63849309
tugal +351-229570200
in +34-915-642095
eden +46-851992065
itzerland
+41-1-4395358 (German)
+41-22-8278780 (French)
+39-02-75419782 (Italian)
ey +420-5-41422523
+44-207-4580161
ch Republic +420-5-41422523
th Africa +27-11-2376200
embourg +32-2-7126219
er European countries +420-5-41422523
untry : Telephone numbers 
tralia +61-3-9841-5211
gapore +61-3-9841-5211
L.America Country : Telephone numbers 
Argentina 0-810-555-5520
Brazil Sao Paulo 3747-7799; 
ROTC 0-800-157751
Mexico Mx City 5258-9922; 
ROTC 01-800-472-6684
Ven
Ch
Co
Per
Ce
Ca
Gu
Pue
Co
N.America Co
U.S
Ca
ROT
Please logon to http:
information.
SG49A.book Page 4 Friday, September 16, 2005 1:31 PM
Page W-4
ezuela 0800-4746-8368
ile 800-360999
lumbia 9-800-114726
u 0-800-10111
ntral America & 
ribbean
1-800-711-2884
atemala 1-800-999-5105
rto Rico 1-877-232-0589
sta Rica 0-800-011-0524
untry : Telephone numbers
. 1800-HP INVENT
nada (905) 206-4663 or 
800- HP INVENT
C = Rest of the country
//www.hp.com for the latest service and support 
Page W-5
Regulatory information
Federal Communications Commission Notice
This equipment has been tested and found to comply with the limits
for a Class B digital device, pursuant to Part 15 of the FCC Rules. These 
limits are designed to provide reasonable protection against harmful 
interference in a residential installation. This equipment generates, uses, 
and can radiate radi
accordance with the 
communications. How
occur in a particula
interference to radio 
turning the equipmen
the interference by on
• Reorient or reloca
• Increase the separ
• Connect the equip
which the receiver
• Consult the dealer
help.
Modifications
The FCC requires the
made to this device 
Company may void t
Cables
Connections to this de
RFI/EMI connector h
regulations.
Declaration of C
Logo, United Stat
This device complies 
the following two c
interference, and (2)
including interference
For questions regardi
Hewlett-Packard Co
P. O. Box 692000,
Houston, Texas 772
SG49A.book Page 5 Friday, September 16, 2005 1:31 PM
o frequency energy and, if not installed and used in 
instructions, may cause harmful interference to radio 
ever, there is no guarantee that interference will not 
r installation. If this equipment does cause harmful 
or television reception, which can be determined by 
t off and on, the user is encouraged to try to correct
e or more of the following measures:
te the receiving antenna.
ation between the equipment and the receiver.
ment into an outlet on a circuit different from that to 
 is connected.
 or an experienced radio or television technician for 
 user to be notified that any changes or modifications 
that are not expressly approved by Hewlett-Packard 
he user’s authority to operate the equipment.
vice must be made with shielded cables with metallic 
oods to maintain compliance with FCC rules and 
onformity for Products Marked with FCC 
es Only
with Part 15 of the FCC Rules. Operation is subject to 
onditions:(1) this device may not cause harmful 
 this device must accept any interference received, 
 that may cause undesired operation.
ng your product, contact:
mpany 
 Mail Stop 530113 
69-2000 
Or, call 
1-800-474-6836 
For questions regarding this FCC declaration, contact: 
Hewlett-Packard Company 
P. O. Box 692000, Mail Stop 510101 
Houston, Texas 77269-2000 
Or, call 
1-281-514-3333 
To identify this prod
on the product.
Canadian Notice
This Class B digital
Canadian Interferenc
Avis Canadien
Cet appareil numér
exigences du Règle
European Union R
This product complies
• Low Voltage Direc
• EMC Directive 89
Compliance with th
harmonized European
EU Declaration of Co
product family.
This compliance is in
on the product:
This compliance is in
on the product: 
This marking is valid for non
and EU harmonized Telecom
Bluetooth).
SG49A.book Page 6 Friday, September 16, 2005 1:31 PM
Page W-6
uct, refer to the part, series, or model number found 
 apparatus meets all requirements of the
e-Causing Equipment Regulations.
ique de la classe B respecte toutes les
ment sur le matériel brouilleur du Canada.
egulatory Notice
 with the following EU Directives:
tive 73/23/EEC
/336/EEC
ese directives implies conformity to applicable 
 standards (European Norms) which are listed on the 
nformity issued by Hewlett-Packard for this product or 
dicated by the following conformity marking placed 
dicated by the following conformity marking placed 
-Telecom prodcts 
 products (e.g. 
 xxxx* 
This marking is valid for EU non-harmonized Telecom products.
*Notified body number (used only if applicable - refer to the 
product label)
Page W-7
Japanese Notice
 この装置は、 情報処理装置等電波障害自主規制協議会 （VCCI） の基準に基づ く ク ラス B 
情報技術装置です。 この装置は、 家庭環境で使用する こ と を目的と し ていますが、 この装
置がラジオやテレビジ ョ ン受信機に近接し て使用される と、 受信障害を引き起こすこ とが
あ り ます。
 取扱説明書に従って正しい取り扱いを し て く だ さい。
Korean Notice
Disposal of W
Private House
This sym
this pr
househ
of your
collectio
electronic equipment
equipment at the tim
and ensure that it is 
the environment. For 
waste equipment for
household waste dis
product.
SG49A.book Page 7 Friday, September 16, 2005 1:31 PM
aste Equipment by Users in 
hold in the European Union
bol on the product or on its packaging indicates that 
oduct must not be disposed of with your other 
old waste. Instead, it is your responsibility to dispose 
 waste equipment by handing it over to a designated 
n point for the recycling of waste electrical and 
. The separate collection and recycling of your waste 
e of disposal will help to conserve natural resources 
recycled in a manner that protects human health and 
more information about where you can drop off your 
 recycling, please contact your local city office, your 
posal service or the shop where you purchased the 
	Table of Contents
	Chapter 1
	Basic Operations
	Batteries
	Turning the calculator on and off
	Adjusting the display contrast
	Contents of the calculator’s display
	Menus
	The TOOL menu
	Setting time and date
	Introducing the calculator’s keyboard
	Selecting calculator modes
	Operating Mode
	Number Format and decimal dot or comma
	Standard format
	Fixed format with decimals
	Scientific format
	Engineering format
	Decimal comma vs. decimal point
	Angle Measure
	Coordinate System
	Selecting CAS settings
	Explanation of CAS settings
	Selecting Display modes
	Selecting the display font
	Selecting properties of the line editor
	Selecting properties of the Stack
	Selecting properties of the equation writer (EQW)
	References
	Chapter 2
	Calculator objects
	Editing expressions in the stack
	Creating arithmetic expressions
	Creating algebraic expressions
	Using the Equation Writer (EQW) to create expressions
	Creating arithmetic expressions
	Creating algebraic expressions
	Organizing data in the calculator
	The HOME directory
	Subdirectories
	Variables
	Typing variable names
	Creating variables
	Algebraic mode
	RPN mode
	Checking variables contents
	Algebraic mode
	RPN mode
	Using the right-shift key followed by soft menu key labels
	Listing the contents of all variables in the screen
	Deleting variables
	Using function PURGE in the stack in Algebraic mode
	Using function PURGE in the stack in RPN mode
	UNDO and CMD functions
	CHOOSE boxes vs. Soft MENU
	References
	Chapter 3
	Examples of real number calculations
	Using powers of 10 in entering data
	Real number functions in the MTH menu
	Using calculator menus
	Hyperbolic functions and their inverses
	Operations with units
	The UNITS menu
	Available units
	Attaching units to numbers
	Unit prefixes
	Operations with units
	Unit conversions
	Physical constants in the calculator
	Defining and using functions
	Reference
	Chapter 4
	Definitions
	Setting the calculator to COMPLEX mode
	Entering complex numbers
	Polar representation of a complex number
	Simple operations with complex numbers
	The CMPLX menus
	CMPLX menu through the MTH menu
	CMPLX menu in keyboard
	Functions applied to complex numbers
	Function DROITE: equation of a straight line
	Reference
	Chapter 5
	Entering algebraic objects
	Simple operations with algebraic objects
	Functions in the ALG menu
	Operations with transcendental functions
	Expansion and factoring using log-exp functions
	Expansion and factoring using trigonometric functions
	Functions in the ARITHMETIC menu
	Polynomials
	The HORNER function
	The variable VX
	The PCOEF function
	The PROOT function
	The QUOT and REMAINDER functions
	The PEVAL function
	Fractions
	The SIMP2 function
	The PROPFRAC function
	The PARTFRAC function
	The FCOEF function
	The FROOTS function
	Step-by-step operations with polynomials and fractions
	Reference
	Chapter 6
	Symbolic solution of algebraic equations
	Function ISOL
	Function SOLVE
	Function SOLVEVX
	Function ZEROS
	Numerical solver menu
	Polynomial Equations
	Finding the solutions to a polynomial equation
	Generating polynomial coefficients given the polynomial's roots
	Generating an algebraic expression for the polynomial
	Financial calculations
	Solving equations with one unknown through NUM.SLV
	Function STEQ
	Solution to simultaneous equations with MSLV
	Reference
	Chapter 7
	Creating and storing lists
	Operations with lists of numbers
	Changing sign
	Addition, subtraction, multiplication, division
	Functions applied to lists
	Lists of complex numbers
	Lists of algebraic objects
	The MTH/LIST menu
	The SEQ function
	The MAP function
	Reference
	Chapter 8
	Entering vectors
	Typing vectors in the stack
	Storing vectors into variables in the stack
	Using the Matrix Writer (MTRW) to enter vectors
	Simple operations with vectors
	Changing sign
	Addition, subtraction
	Multiplication by a scalar, and division by a scalar
	Absolute value function
	The MTH/VECTOR menu
	Magnitude
	Dot product
	Cross product
	Reference
	Chapter 9
	Entering matrices in the stack
	Using the Matrix Writer
	Typing in the matrix directly into the stack
	Operations with matrices
	Addition and subtraction
	Multiplication
	Multiplication by a scalar
	Matrix-vector multiplication
	Matrix multiplication
	Term-by-term multiplication
	Raising a matrix to a real power
	The identity matrix
	The inverse matrix
	Characterizing a matrix (The matrix NORM menu)
	Function DET
	Function TRACE
	Solution of linear systems
	Using the numerical solver for linear systems
	Solution with the inverse matrix
	Solution by “division” of matrices
	References
	Chapter 10
	Graphs options in the calculator
	Plotting an expression of the form y = f(x)
	Generating a table of values for a function
	Fast 3D plots
	Reference
	Chapter 11
	The CALC (Calculus) menu
	Limits and derivatives
	Function lim
	FunctionsDERIV and DERVX
	Anti-derivatives and integrals
	Functions INT, INTVX, RISCH, SIGMA and SIGMAVX
	Definite integrals
	Infinite series
	Functions TAYLR, TAYLR0, and SERIES
	Reference
	Chapter 12
	Partial derivatives
	Multiple integrals
	Reference
	Chapter 13
	The del operator
	Gradient
	Divergence
	Curl
	Reference
	Chapter 14
	The CALC/DIFF menu
	Solution to linear and non-linear equations
	Function LDEC
	Function DESOLVE
	The variable ODETYPE
	Laplace Transforms
	Laplace transform and inverses in the calculator
	Fourier series
	Function FOURIER
	Fourier series for a quadratic function
	Reference
	Chapter 15
	The MTH/PROBABILITY.. sub-menu - part 1
	Factorials, combinations, and permutations
	Random numbers
	The MTH/PROB menu - part 2
	The Normal distribution
	The Student-t distribution
	The Chi-square distribution
	The F distribution
	Reference
	Chapter 16
	Entering data
	Calculating single-variable statistics
	Sample vs. population
	Obtaining frequency distributions
	Fitting data to a function y = f(x)
	Obtaining additional summary statistics
	Confidence intervals
	Hypothesis testing
	Reference
	Chapter 17
	The BASE menu
	Writing non-decimal numbers
	Reference
	Chapter 18
	Inserting and removing an SD card
	Formatting an SD card
	Accessing objects on an SD card
	Storing objects on the SD card
	Recalling an object from the SD card
	Purging an object from the SD card
	Purging all objects on the SD card (by reformatting)
	Specifying a directory on an SD card
	Chapter 19
	Reference
	Limited Warranty
	Service
	Regulatory information
	Disposal of Waste Equipment by Users in Private Household in the European Union