Introduction to Partial Differential Equations A Computational Approach~tqw~ darksiderg

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Introduction to Partial Differential Equations: A Computational Approach
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Release NotesThis 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.

Table Of Contents

1 Setting the Scene 1
2 Two-Point Boundary Value Problems 39
3 The Heat Equation 87
4 Finite Difference Schemes for the Heat Equation 117
5 The Wave Equation 159
6 Maximum Principles 175
7 Poisson's Equation in Two Space Dimensions 209
8 Orthogonality and General Fourier Series 245
9 Convergence of Fourier Series 285
10 The Heat Equation Revisited 313
11 Reaction-Diffusion Equations 337
12 Applications of the Fourier Transform 365
References 385
Index 389

Product Details

* ISBN: 354022551X
* ISBN-13: 9783540225515
* Format: Hardcover, 392pp
* Publisher: Springer-Verlag New York, LLC
* Pub. Date: November 2004
* Edition Number: 2
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