Applied Mathematics for Engineers and Physicists: Third Edition

By: Prof. Louis A. Pipes, Dr. Lawrence R. Harvill



One of the most widely used reference books on applied mathematics for a generation, distributed in multiple languages throughout the world, this text is geared toward use with a one-year advanced course in applied mathematics for engineering students. The treatment assumes a solid background in the theory of complex variables and a familiarity with complex numbers, but it includes a brief review. Chapters are as self-contained as possible, offering instructors flexibility in designing their own courses.

The first eight chapters explore the analysis of lumped parameter systems. Succeeding topics include distributed parameter systems and important areas of applied mathematics. Each chapter features extensive references for further study as well as challenging problem sets. Answers and hints to select problem sets are included in an Appendix. This edition includes a new Preface by Dr. Lawrence R. Harvill.

CONTENTS

Chapter 1 THE THEORY OF COMPLEX VARIABLES
Chapter 2 LINEAR DIFFERENTIAL EQUATIONS
Chapter 3 LINEAR ALGEBRAIC EQUATIONS, DETERMINANTS, AND MATRICES
Chapter 4 LAPLACE TRANSFORMS
Chapter 5 OSCILLATIONS OF LINEAR LUMPED ELECTRICAL CIRCUITS
Chapter 6 OSCILLATIONS OF LINEAR MECHANICAL SYSTEMS
Chapter 7 THE CALCULUS OF FINITE DIFFERENCES AND LINEAR DIFFERENCE EQUATIONS WITH CONSTANT COEFFICIENTS
Chapter 8 TRANSFER FUNCTIONS AND IMPULSE RESPONSES
Chapter 9 LAPLACE’S EQUATION
Chapter 10 THE SOLUTION OF TWO-DIMENSIONAL POTENTIAL PROBLEMS BY THE METHOD OF CONJUGATE FUNCTIONS
Chapter 11 THE EQUATION OF HEAT CONDUCTION OR DIFFUSION
Chapter 12 THE WAVE EQUATION
Chapter 13 OPERATIONAL METHODS IN APPLIED MATHEMATICS
Chapter 14 APPROXIMATE METHODS IN APPLIED MATHEMATICS
Chapter 15 THE ANALYSIS OF NONLINEAR SYSTEMS
Chapter 16 STATISTICS AND PROBABILITY

Appendix A TABLE OF LAPLACE TRANSFORMS
Appendix B SPECIAL FUNCTIONS OF APPLIED MATHEMATICS
Appendix C INFINITE SERIES, FOURIER SERIES, AND FOURIER INTEGRALS
Appendix D THE SOLUTION OF TRANSCENDENTAL AND POLYNOMIAL EQUATIONS
Appendix E VECTOR AND TENSOR ANALYSIS
Appendix F PARTIAL DIFFERENTIATION AND THE CALCULUS OF VARIATIONS
Appendix G ANSWERS TO SELECTED PROBLEMS

INDEX