Introduction to Partial Differential Equations: A Computational Approach: 29 (Texts in Applied Mathematics, 29) - Hardcover

Tveito, Aslak; Winther, Ragnar

Hardcover

ISBN 10: 354022551X ISBN 13: 9783540225515

Publisher: Springer, 2004

Synopsis

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.

About this title

Product Description

This book teaches basic methods of partial differential equations and introduces related important ideas associated with the analysis of numerical methods for those partial differential equations. Coverage details such topics as separation of variables, Fourier analysis, maximum principles, and energy estimates. The book introduces numerical methods in parallel to the classical theory and also includes many engaging exercises.

Review

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 Handlovicová, Zentralblatt MATH, 1063, 2005)

Edition details

• Publisher: Springer
• Publication date: 2004
• ISBN 10: 354022551X
• ISBN 13: 9783540225515
• Binding: Hardcover
• Language: English
• Edition number: 1
• Number of pages: 410