Partial Differential Equations

Analytical and Numerical Methods

Mark S. Gockenbach

636 pages, parution le 15/10/2002

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Résumé

This introductory text on partial differential equations is the first to integrate modern and classical techniques for solving PDEs at a level suitable for undergraduates. The author successfully complements the classical topic of Fourier series with modern finite element methods. The result is an up-to-date, powerful, and flexible approach to solving PDEs, which both faculty and students will find refreshing, challenging, and rewarding.

Linear algebra is a key component of the text, providing a framework both for computing solutions and for understanding the theoretical basis of the methods. Although techniques are emphasized over theory, the methods are presented in a mathematically sound fashion to develop a strong foundation for further study. Numerous exercises and examples involve meaningful experiments with realistic physical parameters, allowing students to use physical intuition to understand the qualitative features of the solutions.

A modern course in PDEs at this level calls for the use of powerful software. Although the text is independent of any particular software package, the accompanying CD-ROM includes thorough tutorials on using Matlab, Mathematica, and Maple to compute and graph solutions.

The subject of partial differential equations is among the most difficult subjects to teach. Partial Differential Equations: Analytical and Numerical Methods has many features to ease the student into the subject:

thorough expositions of the background material from linear algebra and ordinary differential equations;
an emphasis on connecting mathematical results with physical understanding;
some of the best tutorial material available for Matlab, Mathematica, and Maple;
solutions to odd-numbered exercises, including, in many cases, a complete outline of the solution process.

Sommaire

Classification of differential equations
Models in one dimension
Essential linear algebra
Essential ordinary differential equations
Boundary value problems in statics
Heat flow and diffusion
Waves
Problems in multiple spatial dimensions
More about Fourier series
More about finite element methods

A - Proof of theorem 3.47
B - Shifting the data in two dimensions
C - Solutions to odd-numbered exercices

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Caractéristiques techniques

	PAPIER
Éditeur(s)	SIAM: Society for Industrial and Applied Mathematics
Auteur(s)	Mark S. Gockenbach
Parution	15/10/2002
Nb. de pages	636
Format	18,5 x 26
Couverture	Relié
Poids	1280g
Intérieur	Noir et Blanc
EAN13	9780898715187
ISBN13	978-0-89871-518-7