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]

  1. Introduction and first examples 100% developed
  2. Transport equation 100% developed
  3. Test functions 100% developed
  4. Distributions 75% developed
  5. Fundamental solutions, Green's functions and Green's kernels 25% developed
  6. Poisson's equation 25% developed
  7. Heat equation 50% developed
  8. The Fourier transform 25% developed
  9. Wave equation
  10. The Malgrange-Ehrenpreis theorem
  11. Characteristic equations
  12. Sobolev spaces 25% developed
  13. Calculus of variations 0% developed
  14. Bochner's Integral
  15. Monotone operators
  16. Answers to the exercises 0% developed
  17. Appendix I: The uniform boundedness principle for (tempered) distributions 0% developed