Partial Differential Equations for Computational Science

This book provides an extensive introduction to the methods and theory of PDEs without relying on the background in functional analysis and differential geometry. In addition to the heat, wave, and Poisson equations, the text also treats some particular systems of particular differential equations: Maxwell's equations, the Navier-Stokes equations, and Navier's equations. It also discusses existence and uniqueness results, Dirichlet forms, weak solutions, and Ritz-Galerkin methods for the heat equation. Appendices in vector analysis, continuum mechanics, and the Maple computer algebra system augment the work.§ While primarily intended for students taking courses at the upper-division and graduate levels of instruction, the book will also be of interest to many professional readers. Maple is set up within the book in such a way that it can be omitted, depending upon the instructor's approach to teaching the course. However, the incorporation of this important computational tool into this work has significant advantages in helping students deal with the subject matter at hand. Therefore, the use of Maple is strongly recommended.§ A multiplatform CD-ROM accompanies the printed text, and is designed to work an Windows 3.1, Windows 95, Macintosh 680x0, Macintosh Power PCs, and most UNIX machines. This disc contains most of the worked examples from the book as Maple Worksheets, delivered in both Release 3 and Release 4 of the Maple software system. The CD also includes a Maple demo which runs on all computer platforms indicated above, and explains the Maple system in some detail.