Introduction to Partial Differential Equations
by John Douglas Moore
Publisher: UCSB 2003
Number of pages: 169
Our goal here is to develop the most basic ideas from the theory of partial differential equations, and apply them to the simplest models arising from physics. In particular, we will present some of the elegant mathematics that can be used to describe the vibrating circular membrane.
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by Erich Miersemann - Leipzig University
These lecture notes are intended as a straightforward introduction to partial differential equations which can serve as a textbook for undergraduate and beginning graduate students. Some material of the lecture notes was taken from some other books.
by R. E. Showalter - Pitman
Written for beginning graduate students of mathematics, engineering, and the physical sciences. It covers elements of Hilbert space, distributions and Sobolev spaces, boundary value problems, first order evolution equations, etc.
by Sigeru Mizohata - Tata Institute of Fundamental Research
A Cauchy problem in mathematics asks for the solution of a partial differential equation that satisfies certain conditions which are given on a hypersurface in the domain. Cauchy problems are an extension of initial value problems.
by J.L. Lions - Tata Institute of Fundamental Research
In these lectures we study the boundary value problems associated with elliptic equation by using essentially L2 estimates (or abstract analogues of such estimates). We consider only linear problem, and we do not study the Schauder estimates.