Partial Differential Equations: Analytical and Numerical Methods, Second Edition

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9780898719352: Partial Differential Equations: Analytical and Numerical Methods, Second Edition
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Partial differential equations (PDEs) are essential for modeling many physical phenomena. This undergraduate textbook introduces students to the topic with a unique approach that emphasizes the modern finite element method alongside the classical method of Fourier analysis.

Additional features of this new edition include broader coverage of PDE methods and applications, with new chapters on the method of characteristics, Sturm-Liouville problems, and Green s functions, and a new section on the finite difference method for the wave equation. The author continues to emphasize Fourier series and finite element methods, which were the primary scope of the first edition.

The book also features emphasis on linear algebra, particularly the idea of best approximation; realistic physical parameters and meaningful experiments for many of the examples and exercises; and tutorials for the most popular software (MATLAB, Mathematica, and Maple) that can be used to reproduce the examples and solve the exercises.

Audience: This book is written for undergraduate courses usually titled Introduction to Partial Differential Equations or Fourier Series and Boundary Value Problems.

Contents: Preface; Chapter 1: Classification of Differential Equations; Chapter 2: Models in One Dimension; Chapter 3: Essential Linear Algebra; Chapter 4: Essential Ordinary Differential Equations; Chapter 5: Boundary Value Problems in Statics; Chapter 6: Heat Flow and Diffusion; Chapter 7: Waves; Chapter 8: First-Order PDEs and the Method of Characteristics; Chapter 9: Green's Functions; Chapter 10: Sturm-Liouville Eigenvalue Problems; Chapter 11: Problems in Multiple Spatial Dimensions; Chapter 12: More about Fourier Series; Chapter 13: More about Finite Element Methods; Appendix A: Proof of Theorem 3.47; Appendix B: Shifting the Data in Two Dimensions; Bibliography; Index.

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Book Description:

An undergraduate course on partial differential equations is found in almost every mathematics department, and this is an important offering to any student on such a course because of its fresh approach incorporating both the modern and the traditional methods of analysing and solving partial differential equations.

About the Author:

Mark S. Gockenbach is Professor and Chair of the Department of Mathematical Sciences at Michigan Technological University. He is the author of Partial Differential Equations: Analytical and Numerical Methods (SIAM, 2002), Understanding and Implementing the Finite Element Method (SIAM, 2006), and Finite-Dimensional Linear Algebra (CRC Press, 2010). His research interests include inverse problems in PDEs and numerical methods and software for large-scale optimization problems.

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Mark S. Gockenbach
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Book Description Society for Industrial Applied Mathematics,U.S., United States, 2011. Hardback. Condition: New. 2nd Revised edition. Language: English . Brand New Book. Undergraduate courses on partial differential equations (PDEs) have traditionally been based on the Fourier series method for analysing and solving PDEs. What this textbook offers is a fresh approach; the traditional method taught alongside the modern finite element method. Both powerful methods are introduced to the reader and emphasised equally. A further beneficial feature of the book is that it uses the language of linear algebra, in particular in emphasising the role of best approximation in function spaces and the idea of an eigenfunction expansion. Its inclusion of realistic physical experiments for many examples and exercises will make the book appealing to science and engineering students, as well as students of mathematics. This second edition has a broader coverage of PDE methods and applications than the first, with the inclusion of chapters on the method of characteristics, Green s functions, Sturm-Liouville problems and a section on finite difference methods. Seller Inventory # AAN9780898719352

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Book Description Society for Industrial Applied Mathematics,U.S., United States, 2011. Hardback. Condition: New. 2nd Revised edition. Language: English . Brand New Book. Undergraduate courses on partial differential equations (PDEs) have traditionally been based on the Fourier series method for analysing and solving PDEs. What this textbook offers is a fresh approach; the traditional method taught alongside the modern finite element method. Both powerful methods are introduced to the reader and emphasised equally. A further beneficial feature of the book is that it uses the language of linear algebra, in particular in emphasising the role of best approximation in function spaces and the idea of an eigenfunction expansion. Its inclusion of realistic physical experiments for many examples and exercises will make the book appealing to science and engineering students, as well as students of mathematics. This second edition has a broader coverage of PDE methods and applications than the first, with the inclusion of chapters on the method of characteristics, Green s functions, Sturm-Liouville problems and a section on finite difference methods. Seller Inventory # AAN9780898719352

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