# 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.

Partial differential equations are equations which describe several 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 function spaces
- Distributions
- Fundamental solutions, Green's functions and Green's kernels
- Poisson's equation
- Heat equation
- Helmholtz' equation
- The Fourier transform
- Wave equation
- Characteristic equations
- Sobolev spaces
- Calculus of variations
- Bochner's Integral
- Monotone operators
- The Malgrange-Ehrenpreis theorem
- Answers to the exercises