Introduction to Partial Differential Equations : A Computational Approach Setting the Scene Two Point Boundary Value Problems The Heat Equation Finite Difference Schemes For The Heat Equation The Wave Equation Maximum Principles Poisson’s Equation in Two Space Dimensions Orthogonality and General Fourier Series Convergence of Fourier Series The Heat Equation Revisited Reaction Diffusion Equations Applications of the Fourier Transform. “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 dierential equations. That decision is a wise one; the laws of nature are written in the language of partial dierential 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 dierential equations would also be an advantage. Introductory courses in partial dierential 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 simplied problems. Students who learn about viii Preface computational techniques on other courses subsequently realize the scope of partial dierential equations beyond paper and pencil.