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

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   Introduction to Partial Differential Equations: A Computational Approach

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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.



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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