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 Bob Terrell
Introductory notes on ordinary and partial differential equations for engineers. The text covers only the most important ideas. Assumed background is calculus and a little physics. Linear algebra is introduced in four of the lectures.
by Jean-Pierre Schneiders - Universite de Liege
These notes introduce the reader to the algebraic theory of systems of partial differential equations on a complex analytic manifold. We start by explaining how to switch from the classical point of view to the point of view of algebraic analysis.
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.
by Jeffrey R. Chasnov - The Hong Kong University of Science &Technology
Contents: A short mathematical review; Introduction to odes; First-order odes; Second-order odes, constant coefficients; The Laplace transform; Series solutions; Systems of equations; Bifurcation theory; Partial differential equations.