Partial Differential Equations

This book offers a self-contained introduction to partial differential equations (PDEs). The Second Edition is rewritten to incorporate years of classroom feedback, to correct errors and to improve clarity. The exposition offers many examples, problems and solutions to enhance understanding.

This self-contained text offers an elementary introduction to partial differential equations (PDEs), primarily focusing on linear equations, and also providing some perspective on nonlinear equations. The classical treatment is mathematically rigorous with a generally theoretical layout, though indications to some of the physical origins of PDEs are made throughout. Large parts of this revised second edition have been streamlined and rewritten to incorporate years of classroom feedback, to correct errors and to improve clarity. The exposition is replete with examples, problems and solutions that complement the material to enhance understanding and solidify comprehension. The only prerequisites are advanced differential calculus and some basic Lp theory. The work functions as a text for advanced undergraduates and graduate students in mathematics, physics, engineering, and the natural sciences, as well as an excellent reference for applied mathematicians and mathematical physicists.

Self-contained, elementary introduction to PDEs, primarily from a classical perspective

This 2nd edition has been streamlined and rewritten to incorporate years of classroom feedback

Examples, problems, and solutions enhance understanding and solidify comprehension

Classical introduction to issues of current investigation

Includes supplementary material: sn.pub/extras

Contenu
Preliminaries.- Quasi-Linear Equations and the Cauchy#x2013;Kowalewski Theorem.- The Laplace Equation.- Boundary Value Problems by Double-Layer Potentials.- Integral Equations and Eigenvalue Problems.- The Heat Equation.- The Wave Equation.- Quasi-Linear Equations of First-Order.- Non-Linear Equations of First-Order.- Linear Elliptic Equations with Measurable Coefficients.- DeGiorgi Classes.