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.

Autorentext
Prof. Aslak Tveito is the managing director of Simula Research Laboratory. His research is focused on computing the electrical activity in the heart.

Klappentext

This book teaches basic methods of partial differential equations and introduces related important ideas associated with the analysis of numerical methods for those partial differential equations. Coverage details such topics as separation of variables, Fourier analysis, maximum principles, and energy estimates. The book introduces numerical methods in parallel to the classical theory and also includes many engaging exercises.

Zusammenfassung

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)

Inhalt

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.