文档介绍：Instructor’s Solutions Manual
PARTIAL DIFFERENTIAL
EQUATIONS
with FOURIER SERIES and
BOUNDARY VALUE PROBLEMS
Second Edition
NAKHLE´ H. ASMAR
University of Missouri
Contents
Preface v
Errata vi
1 A Preview of Applications and Techniques 1
What Is a Partial Differential Equation? 1
Solving and Interpreting a Partial Differential Equation 4
2 Fourier Series 13
Periodic Functions 13
Fourier Series 21
Fourier Series of Functions with Arbitrary Periods 35
Half-Range Expansions: The Cosine and Sine Series 51
Mean Square Approximation and Parseval’s Identity 58
Form of Fourier Series 63
Forced Oscillations 73
Supplement on Convergence
Uniform Convergence and Fourier Series 79
Dirichlet Test and Convergence of Fourier Series 81
3 Partial Differential Equations in Rectangular Coordinates 82
Partial Differential Equations in Physics and Engineering 82
Solution of the One Dimensional Wave Equation:
The Method of Separation of Variables 87
D’Alembert’s Method 104
The One Dimensional Heat Equation 118
Heat Conduction in Bars: Varying the Boundary Conditions 128
The Two Dimensional Wave and Heat Equations 144
Laplace’s Equation in Rectangular Coordinates 146
Poisson’s Equation: The Method of Eigenfunction Expansions 148
Neumann and Robin Conditions 151
4 Partial Differential Equations in
Polar and Cylindrical Coordinates 155
The Laplacian in Various Coordinate Systems 155
Contents iii
Vibrations of a Circular Membrane: Symmetric Case 228
Vibrations of a Circular Membrane: General Case 166
Laplace’s Equation in Circular Regions 175
Laplace’s Equation in a Cylinder 191
The Helmholtz and Poisson Equations 197
Supplement on Bessel Functions
Bessel’s Equation and Bessel Functions 204
Bessel Series Expansions 213
Integral Formulas and Asymptotics for Bessel Functions 228
5 Partial Di