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Introduction to Partial Differential Equations

A Computational Approach

  • Textbook
  • © 1998

Overview

Authors:
  1. Aslak Tveito

    1. Department of Informatics, Oslo University, Oslo, Norway

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    You can also search for this author in PubMed   Google Scholar

  2. Ragnar Winther

    1. Department of Informatics, Oslo University, Oslo, Norway

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Texts in Applied Mathematics (TAM, volume 29)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xv
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  2. Setting the Scene

    Pages 1-37

  3. Two-Point Boundary Value Problems

    Pages 39-86

  4. The Heat Equation

    Pages 87-116

  5. Finite Difference Schemes For The Heat Equation

    Pages 117-158

  6. The Wave Equation

    Pages 159-173

  7. Maximum Principles

    Pages 175-207

  8. Poisson’s Equation in Two Space Dimensions

    Pages 209-244

  9. Orthogonality and General Fourier Series

    Pages 245-284

  10. Convergence of Fourier Series

    Pages 285-312

  11. The Heat Equation Revisited

    Pages 313-336

  12. Reaction-Diffusion Equations

    Pages 337-364

  13. Applications of the Fourier Transform

    Pages 365-384

  14. Back Matter

    Pages 385-392
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About this book

“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 di?erential equations. That decision is a wise one; the laws of nature are written in the language of partial di?erential equations. Therefore, these equations arise as models in virtually all branches of science and technology. Our goal in this book is to help you to understand what this vast subject is about. The book is an introduction to the ?eld. We assume only that you are familiar with - sic calculus and elementary linear algebra. Some experience with ordinary di?erential equations would also be an advantage. Introductory courses in partial di?erential equations are given all over the world in various forms. The traditional approach to the subject is to introduce a number of analytical techniques, enabling the student to - rive exact solutions of some simpli?ed problems. Students who learn about viii Preface computational techniques on other courses subsequently realize the scope of partial di?erential equations beyond paper and pencil.

Authors and Affiliations

  • Department of Informatics, Oslo University, Oslo, Norway

    Aslak Tveito, Ragnar Winther

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