Introduction to Partial Differential Equations

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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“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.

• Boundary value problem
• Fourier series
• Maximum
• calculus
• differential equation
• numerical methods
• partial differential equation
• wave equation

• Department of Informatics, Oslo University, Oslo, Norway

  Aslak Tveito, Ragnar Winther

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