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Preface | p. xi |
Acknowledgments | p. xiii |
Review of Analytic Function Theory | p. 1 |
Preamble | p. 1 |
Fundamentals of Complex Numbers | p. 1 |
Analytic Functions | p. 4 |
Integration and Cauchy's Theorem | p. 8 |
Application to Real Integrals | p. 19 |
References | p. 30 |
Exercises | p. 30 |
Special Functions | p. 37 |
Preamble | p. 37 |
The Gamma Function | p. 39 |
Functions Defined by Differential Equations | p. 43 |
Integral Representations | p. 51 |
References | p. 55 |
Exercises | p. 55 |
Eigenvalue Problems and Eigenfunction Expansions | p. 62 |
Preamble | p. 62 |
Synge's Setup for Rayleigh's Criterion | p. 62 |
Sturm-Liouville Problems | p. 65 |
Expansions in Eigenfunctions | p. 71 |
Worked Examples | p. 74 |
Nonstandard Eigenvalue Problems | p. 78 |
Fourier-Bessel Series | p. 85 |
Continuous versus Discrete Spectra | p. 91 |
References | p. 94 |
Exercises | p. 95 |
Green's Functions for Boundary-Value Problems | p. 106 |
Preamble | p. 106 |
Green's Function | p. 110 |
Connections with Distributions | p. 119 |
First-Order System: Green's Matrices | p. 121 |
Generalized Green's Functions | p. 122 |
Expansions in Eigenfunctions | p. 125 |
References | p. 132 |
Exercises | p. 133 |
Appendix: Linear Ordinary Differential Equations | p. 142 |
Laplace Transform Methods | p. 148 |
Preamble | p. 148 |
The Laplace Transform and Its Inverse | p. 148 |
Worked Examples | p. 156 |
Bilateral Laplace Transform | p. 171 |
References | p. 175 |
Exercises | p. 176 |
Fourier Transform Methods | p. 183 |
Preamble | p. 183 |
The Fourier Transform and Its Inverse | p. 183 |
Worked Examples | p. 188 |
Mellin Transforms | p. 200 |
Worked Examples | p. 205 |
References | p. 207 |
Exercises | p. 208 |
Particular Physical Problems | p. 217 |
Preamble | p. 217 |
Lee Waves | p. 217 |
The Far Momentum Wake | p. 220 |
Kelvin-Helmholtz Instability | p. 223 |
The Boundary-Layer Signal Problem | p. 225 |
Stability of Plane Couette Flow | p. 228 |
Generalized Transform Techniques | p. 231 |
References | p. 235 |
Exercises | p. 236 |
Asymptotic Expansions of Integrals | p. 244 |
Preamble | p. 244 |
Asymptotic Expansions | p. 244 |
Integration by Parts | p. 245 |
Laplace-Type Integrals; Watson's Lemma | p. 246 |
Generalized Laplace Integrals: Laplace's Method | p. 253 |
Method of Steepest Descent | p. 256 |
Method of Stationary Phase; Kelvin's Results | p. 266 |
References | p. 268 |
Exercises | p. 268 |
Index | p. 279 |
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The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.