Introduction to Partial Differential Equations

1. Front Matter

   Pages i-xv

   PDF

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 385-400

    PDF

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.

• Boundary value problem
• Fourier series
• calculus
• finite difference methods
• maximum principles
• partial differential equation
• partial differential equations
• reaction-diffusion equations
• wave equation

From the reviews:

"Presents an introductory course to study partial differential equations especially from the computational point of view. … At the end of each chapter the reader can find a very good selection of fine exercises or projects ... . The language of the book is simple and easy to read which will be highly appreciated by its readers. The book can be very useful for undergraduate and graduate students in mathematics and engineering." (Angela Handlovicová, Zentralblatt MATH, 1063, 2005)

• Control and Dynamical Systems, 107-81, California Institute of Technology, Pasadena, USA

  J.E. Marsden

• Division of Applied Mathematics, Brown University, Providence, USA

  L. Sirovich

• Department of Mathematics, University of Houston, Houston, USA

  M. Golubitsky

• Department of Applied Mathematics, Universität Heidelberg, Heidelberg, Germany

  W. Jäger

• Simula Research Laboratory, Lysaker, Norway

  Aslak Tveito

• Centre of Mathematics for Applications and Department of Informatics, University of Oslo, Oslo, Norway

  Ragnar Winther

Policies and ethics