lista 1 18 2

Prévia do material em texto

Disciplina: Equações Diferenciais
Lista de Exercícios No 1
Encontre a transformada de Laplace inversa da função dada:
a) 
			 b) 
		
c) 
			d) 
			
e) 
 L constante	f) 
		 
g) 
			h) 
	
i) 
	 	 		j) 
	
Use a transformada de Laplace para resolver o problema de valor inicial:
a) 
b) 
c) 
d) 
e) 
 
f) 
 
Encontre a transformada de Laplace inversa da função dada:
a) 
	b) 
		c) 
d) 
	e) 
	f) 
	
g) 
	
Use a transformada de Laplace para resolver o problema de valor inicial:
a) 
b) 
c) 
d) 
e) 
f) 
 
Esboce o gráfico da função dada e encontre a sua transformada de Laplace:
a) 
	 b) 
		c) 
	
d) 
	e) 
f) 
	g) 
	 h) 
Encontre a transformada de Laplace inversa da função dada:
a) 
		b) 
	c) 
d) 
 e) 
 f) 
Resolva o problema de valor inicial proposto:
a) 
, 
b) 
 
c) 
 
d) 
, 
e) 
f) 
 
8- Calcule a transformada de Laplace de cada função periódica:
a) 
 b) 
 
 
9- Resolva o problema de valor inicial:
 onde 
 
Encontre a transformada de Laplace da função dada (sem resolver a integral):
a) 
		b) 
c) 
		d) 
Escreva a solução do problema de valor inicial em termos de uma integral de convolução:
a) 
b) 
c) 
d) 
Use a transformada de Laplace para resolver a equação integral:
a) 
		b) 
	
c) 
		d) 
	
Resolva o problema de valor inicial proposto:
a) 
b) 
c) 
d) 
e) 
Respostas
1- a) 
	b) 
	c) 
d) 
	e) 
	f) 
g) 
		h) 
	i) 
j) 
 
2-a)
 b)
 c) 
 d) 
	e) 
 f) 
	
3- a) 
		b) 
	c) 
d) 
	e) 
	
f) 
	 g) 
	
4- a) 
	 b) 
	 c) 
	
d) 
e) 
 f) 
		
5- a) 
		
b) 
 c) 
 d) 
 
e) 
 f)
 g) 
 h) 
6- a) 
		b) 
	
c) 
	
d) 
e) 
		f) 
7- a) 
b) 
	c) 
d) 
 
e) 
 onde 
 f) 
 onde 
8- a) 
 b) 
9- 
 10- a) 
 b) 
 
 c)
 d) 
	 
 11- a) 
 b) 
c) 
d) 
12- a) 
 	 b) 
	 
c) 
 d) 
 
 
13- a) 
b) 
c) 
d) 
	e) 
	Transformadas de Laplace
	
ℒ
	
ℒ
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