Ebook: Introduction to Partial Differential Equations: A Computational Approach

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the cl- sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Ma- ematical Sciences (AMS) series, which will focus on advanced textbooks and research-level monographs. Preface "It is impossible to exaggerate the extent to which modern applied mathematics has been shaped and fueled by the g- eral availability of fast computers with large memories. Their impact on mathematics, both applied and pure, is comparable to the role of the telescopes in astronomy and microscopes in biology." — Peter Lax, Siam Rev. Vol. 31 No. 4 Congratulations! You have chosen to study partial differential equations.

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This is the softcover reprint of a popular book teaching the basic analytical and computational methods of partial differential equations. Standard topics such as separation of variables, Fourier analysis, maximum principles, and energy estimates are included. Prerequisites for this text are the very basics of calculus, linear algebra and ordinary differential equations. 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 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 exercises and projects ranging from the straightforward to the challenging. The text would be suitable for advanced undergraduate and graduate courses in mathematics and engineering, and it develops basic tools of computational science.

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This is the softcover reprint of a popular book teaching the basic analytical and computational methods of partial differential equations. Standard topics such as separation of variables, Fourier analysis, maximum principles, and energy estimates are included. Prerequisites for this text are the very basics of calculus, linear algebra and ordinary differential equations. 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 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 exercises and projects ranging from the straightforward to the challenging. The text would be suitable for advanced undergraduate and graduate courses in mathematics and engineering, and it develops basic tools of computational science.

Content:
Front Matter....Pages i-xv
Setting the Scene....Pages 1-37
Two-Point Boundary Value Problems....Pages 39-86
The Heat Equation....Pages 87-116
Finite Difference Schemes for the Heat Equation....Pages 117-158
The Wave Equation....Pages 159-173
Maximum Principles....Pages 175-207
Poisson's Equation in Two Space Dimensions....Pages 209-244
Orthogonality and General Fourier Series....Pages 245-284
Convergence of Fourier Series....Pages 285-312
The Heat Equation Revisited....Pages 313-336
Reaction-Diffusion Equations....Pages 337-364
Applications of the Fourier Transform....Pages 365-384
Back Matter....Pages 385-400

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This is the softcover reprint of a popular book teaching the basic analytical and computational methods of partial differential equations. Standard topics such as separation of variables, Fourier analysis, maximum principles, and energy estimates are included. Prerequisites for this text are the very basics of calculus, linear algebra and ordinary differential equations. 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 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 exercises and projects ranging from the straightforward to the challenging. The text would be suitable for advanced undergraduate and graduate courses in mathematics and engineering, and it develops basic tools of computational science.

Content:
Front Matter....Pages i-xv
Setting the Scene....Pages 1-37
Two-Point Boundary Value Problems....Pages 39-86
The Heat Equation....Pages 87-116
Finite Difference Schemes for the Heat Equation....Pages 117-158
The Wave Equation....Pages 159-173
Maximum Principles....Pages 175-207
Poisson's Equation in Two Space Dimensions....Pages 209-244
Orthogonality and General Fourier Series....Pages 245-284
Convergence of Fourier Series....Pages 285-312
The Heat Equation Revisited....Pages 313-336
Reaction-Diffusion Equations....Pages 337-364
Applications of the Fourier Transform....Pages 365-384
Back Matter....Pages 385-400
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