Harold Levine

Partial differential equations

Introduction Partial differentiation Solutions of PDEs and their specification PDEs and related arbitrary functions Particular solutions of PDEs Similarity solutions Correctly set problems Some preliminary aspects of linear first order PDEs First order PDEs, linear First order nonlinear PDEs Some technical problems and related PDEs First order PDEs, general theory First order PDEs 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 ODEs Boundary value problems and Sturm-Liouville theory Greens functions and boundary value problems Greens functions and generalizations PDEs, Greens 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.