Partial Differential Equations

Contents Linear partial differential equations Nonlinear partial differential equations /Elliptic equations/ Another old table of contents /Introduction/ /Method of characteristics/ /Calculus of variations/ /Fourier-analytic methods/ (requires Fourier analysis) /The wave equation/ (requires integration on manifolds) /Fundamental solutions/ (requires distribution theory) /Poisson's equation/ (requires integration on manyfolds and harmonic function theory) /The heat equation/ /Sobolev spaces/ (requires some functional analysis) /Monotone operators/ (requires convex analysis) Old table of Contents Authors should be aware of the stylistic guidelines. 300px|right /Introduction and first examples/ 100% Linear partial differential equations /The transport equation/ 100% /Test functions/ 100% /Distributions/ 100% /Fundamental solutions, Green's functions and Green's kernels/ 100% /The heat equation/ 75% /Poisson's equation/ 25% /The Fourier transform/ 75% /The wave equation/ 0% /The Malgrange-Ehrenpreis theorem/ 50% Nonlinear partial differential equations /The characteristic equations/ 0% /Sobolev spaces/ 25% /Convex analysis/ 0% /Calculus of variations/ 0% /Bochner's Integral/ 0% /Monotone operators/ 0% /Answers to the exercises/ 0% /Appendix I: The uniform boundedness principle for (tempered) distributions/ 0% P Mathematical analysis University level mathematics books 25%