| Introduction |
| Partial differentiation Solutions of PDE's and their specification PDE's and related arbitrary functions Particular solutions of PDE's |
| Similarity solutions |
| Correctly set problems |
| Some preliminary aspects of linear first order PDE's |
| First order PDE's, linear First order nonlinear PDE's |
| Some technical problems and related PDE's |
| First order PDE's, general theory |
| First order PDE's with multiple independent variables |
| Original detaials of the Fourier approach to boundary value problems |
| Eigenfunctions and eigenvalues |
| Eigenfunctions and eigenvalues, continued |
| Non-orthogonal eigenfunctions |
| Further example of Fourier style analysis |
| Inhomogeneous problems |
| Local heat sources |
| An inhomogeneous configuration |
| Other eigenfunction/eigenvalue problems |
| Uniqueness of solutions |
| Alternative representations of solutions |
| Other differential equations and inferences therefrom |
| Second order ODE's |
| Boundary value problems and Sturm-Liouville theory |
| Green's functions and boundary value problems |
| Green's functions and generalizations PDE's, Green's functions, and integral equations |
| Singular and infinite range problems |
| Orthogonality and its ramifications |
| Fourier expansions: Generalities |
| Fourier expansions: Varied examples Fourier integrals and transforms |
| Applications of Fourier transforms |
| Legendre polynomials and related expansions |
| Bessel functions and related expansions |
| Hyperbolic equations |
| Afterwords |
| Bibliography |
| Index |
| Introduction |
| Partial differentiation Solutions of PDE's and their specification PDE's and related arbitrary functions Particular solutions of PDE's |
| Similarity solutions |
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