# Partial Differential Equations

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This Wikibook is UNDER CONSTRUCTION! It will hopefully be completed ~~in the months August and September of 2014~~ in the winter term 2014/2015.

Some partial differential equations describe important processes in nature. This wikibook shows how to solve different kinds of partial differential equations and/or gives existence and uniqueness results, using a variety of methods.

Authors should be aware of the stylistic guidelines.

## Table of Contents[edit]

- Introduction and first examples
- Transport equation
- Test functions
- Distributions
- Fundamental solutions, Green's functions and Green's kernels
- Poisson's equation
- Heat equation
- The Fourier transform
- Wave equation
- The Malgrange-Ehrenpreis theorem
- Characteristic equations
- Sobolev spaces
- Calculus of variations
- Bochner's Integral
- Monotone operators
- Answers to the exercises
- Appendix I: The uniform boundedness principle for (tempered) distributions