PREFACE_1970_Differential-Forms-on-Electromagnetic-Networks

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PREFACE 
THE subject matter of this book is largely a theoretical treatment of 
electrical circuits and the magnetic fields which surround them. 
The mathematical methods presented here are not yet widely 
used in engineering analysis. They are, however, elegant and quite 
powerful and can be applied to advantage in many field problems. 
The theory of differential forms is usually treated by a purely 
mathematical approach, but the present authors have adopted an 
engineering orientation. They have endeavoured to associate the 
mathematics with physical concepts, built around one particular 
model—the electromagnetic network—in an attempt to bring 
vector and tensor relationships to life. Thus, although the book is 
primarily intended to contribute to electrical engineering it should 
be of assistance to teachers and undergraduate and postgraduate 
students of appHed mathematics and physics. 
The machine and circuit models and much of the tensor analysis 
described here were originally developed by the late Dr. Gabriel 
Kron. It is the authors' belief that both the basic theory and more 
sophisticated structures, built around these models, will become of 
increasing importance, especially in relation to spatially distributed 
continuous systems. Obviously much of the more recent mathemati­
cal theory stems from the published work of others and the authors 
÷ PREFACE 
acknowledge their debt in this respect, especially to two sources, 
namely references 16 and 17. 
They also express their thanks to their associates at the University 
of Liverpool for useful discussion in formulating and clarifying 
various aspects of the theory; in particular to Dr. T. A. S. Jackson 
of the Department of Applied Mathematics and Dr. S. A. Robertson 
of the Department of Pure Mathematics; to Mr. M . Yau, who 
carried out some of the machine tests, to the stafiT of the Computer 
Laboratory, to Miss A. Ennis who typed the manuscript, and to 
Miss A. E. Howarth, Assistant Librarian in the Faculty of Engineer­
ing Science, for the translation of reference 42. They are indebted 
to Mr. E. E. Dweck for valuable criticism and discussion. 
They also express their appreciation of the assistance given to 
them by the publishers for advice at all stages in the process of 
publication. 
Liverpool 
N . V. Balasubramanian 
J. W. Lynn 
D. P. Sen Gupta