Partial Differential Equations

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This is book is currently under a complete redesign to focus the material toward the pure mathematical development of the field of partial differential equations. The book previously called partial differential equations has been moved to Advanced Mathematics for Engineers and Scientists.

Table of Contents[edit]

Introduction and first examples

Distributions

Sobolev spaces

Fundamental Solutions, Green's functions, Green's kernels and Dirichlet Problems

Poisson's equation

Heat equation

Transport equation

Wave equation

Calculus of variations

Theorem of Malgrange-Ehrenpreis

Appendix[edit]

Lemma 2.1: Banach-Steinhaus theorem for locally convex sets