Mathematics for electronics : with applications

404 Pages·1956·33.705 MB·English

by  Nodelman, Henry M., Smith, Frederick Whittle

NODELMAN and SMITH
MATHEMATICS FOR ELECTRONICS WITH APPLICATIONS

MATHEMATICS
for ELECTRONICS
with Applications
HENRY M. NODELMAN
Head of Mathematics and Physics Departments
RCA Institutes, and Instructor in Mathematics,
Polytechnic Institute of Brooklyn
FREDERICK W. SMITH
Television Engineer f
National Broadcasting Company
MCGRAW-HILL BOOK COMPANY, INC.
Xew York Toronto London
19 5 6
MATHEMATICS TOR ELECTRONICS
with Applications
Copyright © 1056 by the McGraw-Hill Book Company, Inc. Printed in the United
States of America. AH rights reserved. This book, or parts thereof, may not be
reproduced in any form without permission of the publishers.
Library of Congress Catalog Card Number 55-9549
IX
4GS50
THE MAPLE PItBSS COMPANY, YOItK, PA.
Preface
In Mathematics for Electronics with Applications, the emphasis has
been placed on application rather than on mathematical theory. This
approach, which represents a new departure for a mathematics text in
this field, is deliberate. It is a direct result of the authors many years
7
of experience in the teaching of mathematics to students of electronic
engineering and in engineering practice. It is our conviction that the
wide barrier which exists between mathematics and its applications can
best be surmounted by demonstrating the practical uses which industry
makes of mathematics. In this way, student motivation is increased
considerably, and the student is not confronted with the problem of
interrelating two discrete sets of information, one mathematical, the
other electronic, as unfortunately has too often been the case.
In order to accomplish this objective, the text offers a complete set of
up-to-date problems based on current engineering practice, the result of
more than five years of research in the technical literature. All of the
leading American and foreign technical periodicals devoted to communi¬
cations and electronics were carefully examined to determine which
mathematical topics were to be included. The mathematical applica¬
tions are accompanied by worked-out examples and are extensively
supported with references so that the reader can supplement his knowledge
of the problem by consulting the original article from which the problem
was obtained.
Part I of the book describes the methods by which mathematics has
been used in electronics and presents a series of electronic engineering
problems which involve the use of the calculus. Part II introduces the
reader to dimensional analysis as it is applied in electronics and shows the
methods which can be used to check the validity of engineering equations
and formulas independent of the engineering considerations used to
establish such equations. Part III deals with the algebra of determi¬
nants. The theory is then applied to the solution of steady-state elec¬
tronic circuits. Matrix algebra is discussed, and the solution of elec¬
tronic networks, including those which contain transistors, is undertaken
by the matrix method. In Part IV the fundamental properties of series
approximations are presented. The use of series to predict the behavior
of nonlinear electronic devices is treated; the processes of harmonic gen-
V[ PREFACE
eration and intermod illation testing are described. Part V is devoted
to solutions of differential equations employing both classical and Laplace
transform methods. Part. VI gives the elements of Boolean algebra and
includes material on switching circuits. In addition, it presents an
analysis of the more advanced mathematical topics which logically
follow those incorporated in the text. The various parts of the book are
independent and may be studied and read as separate units if desired.
The book is intended for those readers who have a background of
elementary calculus, physics, and elementary electrical network theory.
It is designed for use in industry as well as for use in undergraduate tech¬
nical institute and engineering college courses in applied mathematics,
networks, transients, and nonlinear systems.
Because the technical references incorporated in this book are such an
integral part of t, it is obvious that the book could not have become a
reality without the generous cooperation of the editors of the various
technical publications identified in the footnote references, for which the
authors are grateful. We also wish to extend thanks to the industrial
organizations elsewhere identified who made illustrations and valuable
technical data available.
Hen by M. Non elman
Fandeuick W. Smith
Con fen fs
Preface v
PART 1* The Uses of Mathematics in Electronics 3
1- ('use Histories of Practical Applications 5
2. Electronic Applications of Calculus 10
PART 2* Equation Testing
prior to Mathematical Operations 37
3. Dimensional Formulas and Systems ' 39
4* Checking Equations
and Predicting Solutions 54
PART 3* The Algebra of Circuit Analysis 79
5. Theory of Determinants 81
6. Network Solutions by Determinants 99
7. Matrix Algebra 155
8. Network Solutions by Matrices 172
PART 4_ Theory and Applications of Series 213
9. Basic Properties and Applications 215
10. Nonlinear Electronic Devices 238
PART 5. Differentia! Equations:
Theory and Applications 259
11. Classical Solutions
and Non-network Applications 261
vii
viii CONTENTS
12. Transient Solutions
and Elementary Laplace Transforms 289
PART 6. The Direction of Mathematics
in Electronics 345
13. Elements of Boolean Algebra 347
14. A Study Plan in Mathematics
for Specialists in Electronics 356
APPENDIX 361
Table A-4. Common Logarithms 363
Table A-2. Natural Logarithms 365
Table A-3. Values of and 366
Table A-4. Trigonometric Functions 367
Table A-5. Integrals 372
Author Index 377
Subject Index 381
MATHEMATICS FOR ELECTRONICS WITH APPLICATIONS