Spectral Theory of Partial Differential Equations
by Richard S. Laugesen
Publisher: arXiv 2012
Number of pages: 120
This mini-course of 20 lectures aims at highlights of spectral theory for self-adjoint partial differential operators, with a heavy emphasis on problems with discrete spectrum. The course aims to develop your mental map of spectral theory in partial differential equations.
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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 R. Bryant, P. Griffiths, D. Grossman - University Of Chicago Press
The authors present the results of their development of a theory of the geometry of differential equations, focusing especially on Lagrangians and Poincare-Cartan forms. They also cover certain aspects of the theory of exterior differential systems.
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 B. Piette - University of Durham
In these notes, we describe the design of a small C++ program which solves numerically the sine-Gordon equation. The program is build progressively to make it multipurpose and easy to modify to solve any system of partial differential equations.