Partial Differential Equations

Nonlinear partial differential equations

 * 1) /Elliptic equations/

Another old table of contents

 * 1) /Introduction/
 * 2) /Method of characteristics/
 * 3) /Calculus of variations/
 * 4) /Fourier-analytic methods/ (requires Fourier analysis)
 * 5) /The wave equation/ (requires integration on manifolds)
 * 6) /Fundamental solutions/ (requires distribution theory)
 * 7) /Poisson's equation/ (requires integration on manyfolds and harmonic function theory)
 * 8) /The heat equation/
 * 9) /Sobolev spaces/ (requires some functional analysis)
 * 10) /Monotone operators/ (requires convex analysis)

Old table of Contents
Authors should be aware of the stylistic guidelines.


 * 1) /Introduction and first examples/

Linear partial differential equations
/The transport equation/  /Test functions/  /Distributions/  /Fundamental solutions, Green's functions and Green's kernels/  /The heat equation/  /Poisson's equation/  /The Fourier transform/  /The wave equation/  <li>/The Malgrange-Ehrenpreis theorem/ </li> </ol>

Nonlinear partial differential equations
<li>/The characteristic equations/ </li> <li>/Sobolev spaces/ </li> <li>/Convex analysis/ </li> <li>/Calculus of variations/ </li> <li>/Bochner's Integral/ </li> <li>/Monotone operators/ </li> </ol>

<li>/Answers to the exercises/ </li> <li>/Appendix I: The uniform boundedness principle for (tempered) distributions/ </li> </ol>