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

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  Introduction to Partial Differential Equations A Computational Approach~tqw~ darksiderg
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  *******************************************************************************<br /> Introduction to Partial Differential Equations: A Computational Approach<br /> *******************************************************************************<br /> <br /> -------------------------------------------------------------------------------<br /> General Information<br /> -------------------------------------------------------------------------------<br /> Type.................: Ebook<br /> Part Size............: 13,098,276 bytes<br /> <br /> <br /> <br /> <br /> -------------------------------------------------------------------------------<br /> Post Information<br /> -------------------------------------------------------------------------------<br /> Posted by............: ~tqw~<br /> <br /> -------------------------------------------------------------------------------<br /> Release Notes<br /> -------------------------------------------------------------------------------<br /> This book teaches the basic methods of partial differential equations and <br /> introduces related important ideas associated with the analysis of numerical <br /> methods for those partial differential equations. Standard topics such as <br /> separation of variables, Fourier analysis, maximum principles, and energy <br /> estimates are included. Numerical methods are introduced in parallel to the <br /> classical theory. The numerical experiments are used to illustrate properties of <br /> differential equations and theory for finite difference approximations is <br /> developed. Numerical methods are included in the book to show the significance <br /> of computations in partial differential equations and to illustrate the strong <br /> interaction between mathematical theory and the development of numerical <br /> methods. Great care has been taken throughout the book to seek a sound balance <br /> between the analytical and numerical techniques. The authors present the <br /> material at an easy pace with well-organized exercises ranging from the <br /> straightforward to the challenging. In addition, special projects are included, <br /> containing step by step hints and instructions, to help guide students in the <br /> correct way of approaching partial differential equations. The text would be <br /> suitable for advanced undergraduate and graduate courses in mathematics and <br /> engineering. Necessary prerequisites for this text are basic calculus and linear <br /> algebra. Some elementary knowledge of ordinary differential equations is also <br /> preferable.<br /> <br /> Table Of Contents<br /> <br /> 1 Setting the Scene 1<br /> 2 Two-Point Boundary Value Problems 39<br /> 3 The Heat Equation 87<br /> 4 Finite Difference Schemes for the Heat Equation 117<br /> 5 The Wave Equation 159<br /> 6 Maximum Principles 175<br /> 7 Poisson's Equation in Two Space Dimensions 209<br /> 8 Orthogonality and General Fourier Series 245<br /> 9 Convergence of Fourier Series 285<br /> 10 The Heat Equation Revisited 313<br /> 11 Reaction-Diffusion Equations 337<br /> 12 Applications of the Fourier Transform 365<br /> References 385<br /> Index 389<br /> <br /> Product Details<br /> <br /> * ISBN: 354022551X<br /> * ISBN-13: 9783540225515<br /> * Format: Hardcover, 392pp<br /> * Publisher: Springer-Verlag New York, LLC<br /> * Pub. Date: November 2004<br /> * Edition Number: 2<br /> <br /> -------------------------------------------------------------------------------<br /> Install Notes<br /> -------------------------------------------------------------------------------<br /> PDF Reader
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