Introduction to Partial Differential Equations

A Computational Approach

Aslak Tveito, Ragnar Winther

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English

Springer Verlag
01 June 2005

Mathematics & Sciences; Differential calculus & equations

Series: Texts in Applied Mathematics

This book teaches the basic methods of partial differential equations and introduces related important ideas associated with the analysis of numerical methods for those partial differential equations. Standard topics such as separation of variables, Fourier analysis, maximum principles, and energy estimates are included. Numerical methods are introduced in parallel to the classical theory. The numerical experiments are used to illustrate properties of differential equations and theory for finite difference approximations is developed. Numerical methods are included in the book to show the significance of computations in partial differential equations and to illustrate the strong interaction between mathematical theory and the development of numerical methods. Great care has been taken throughout the book to seek a sound balance between the analytical and numerical techniques. The authors present the material at an easy pace with well-organized exercises ranging from the straightforward to the challenging. In addition, special projects are included, containing step by step hints and instructions, to help guide students in the correct way of approaching partial differential equations. The text would be suitable for advanced undergraduate and graduate courses in mathematics and engineering. Necessary prerequisites for this text are basic calculus and linear algebra. Some elementary knowledge of ordinary differential equations is also preferable.

By: Aslak Tveito, Ragnar Winther
Imprint: Springer Verlag
Country of Publication: Germany
Dimensions: Height: 235mm, Width: 155mm, Spine: 23mm
Weight: 827g
ISBN: 9783540225515
ISBN 10: 354022551X
Series: Texts in Applied Mathematics
Publication Date: 01 June 2005
Audience: College/higher education , A / AS level
Format: Hardback
Publisher's Status: Active

Setting the Scene.- Two-Point Boundary Value Problems.- The Heat Equation.- Finite Difference Schemes for the Heat Equation.- The Wave Equation.- Maximum Principles.- Poisson's Equation in Two Space Dimensions.- Orthogonality and General Fourier Series.- Convergence of Fourier Series.- The Heat Equation Revisited.- Reaction-Diffusion Equations.- Applications of the Fourier Transform.

Reviews for Introduction to Partial Differential Equations: A Computational Approach

From the reviews: Presents an introductory course to study partial differential equations especially from the computational point of view. ... At the end of each chapter the reader can find a very good selection of fine exercises or projects ... . The language of the book is simple and easy to read which will be highly appreciated by its readers. The book can be very useful for undergraduate and graduate students in mathematics and engineering. (Angela Handlovicova, Zentralblatt MATH, 1063, 2005)