Introduction to Partial Differential Equations
by Valeriy Serov
Publisher: University of Oulu 2011
Number of pages: 122
Contents: Preliminaries; Local Existence Theory; Fourier Series; One-dimensional Heat Equation; One-dimensional Wave Equation; Laplace Equation in Rectangle and in Disk; The Laplace Operator; The Dirichlet and Neumann Problems; Layer Potentials; The Heat Operator; The Wave Operator.
Download or read it online for free here:
by Vicentiu Radulescu - arXiv
This textbook provides the background which is necessary to initiate work on a Ph.D. thesis in Applied Nonlinear Analysis. The purpose is to provide a broad perspective in the subject. The level is aimed at beginning graduate students.
by Per Jakobsen - arXiv
These lecture notes give an introduction to perturbation method with main focus on the method of multiple scales as it applies to pulse propagation in nonlinear optics. Aimed at students that have little or no background in perturbation methods.
by Lawrence C. Evans - UC Berkeley
This course surveys various uses of 'entropy' concepts in the study of PDE, both linear and nonlinear. This is a mathematics course, the main concern is PDE and how various notions involving entropy have influenced our understanding of PDE.
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.