Introduction to partial differential equations : a computational approach
 Responsibility
 Aslak Tveito, Ragnar Winther.
 Language
 English.
 Imprint
 New York : Springer, c1998.
 Physical description
 xv, 392 p. : ill. ; 24 cm.
 Series
 Texts in applied mathematics 29.
Access
Creators/Contributors
 Author/Creator
 Tveito, Aslak, 1961
 Contributor
 Winther, Ragnar.
Contents/Summary
 Bibliography
 Includes bibliographical references (p. [385]387) and index.
 Contents

 Setting the scene * Twopoint boundary value problems * The heat equation * Finite difference schemes * 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 * ReactionDiffusion Equations * Applications of the Fourier transform * References * Index.
 (source: Nielsen Book Data)
 Publisher's Summary
 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 wellorganized 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.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 1998
 Series
 Texts in applied mathematics ; 29
 ISBN
 0387983279 (hardcover : acidfree paper)
 9780387983271 (hardcover : acidfree paper)