Introduction to Partial Differential Equations

A Computational Approach
Buch | Hardcover
XVI, 394 Seiten
2004 | 1st ed. 1998. Corr. 2nd printing 2004
Springer Berlin (Verlag)
978-3-540-22551-5 (ISBN)
80,24 inkl. MwSt
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.

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

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.

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)

Erscheint lt. Verlag 4.10.2004
Reihe/Serie Texts in Applied Mathematics
Zusatzinfo XVI, 394 p.
Verlagsort Berlin
Sprache englisch
Maße 155 x 235 mm
Gewicht 740 g
Themenwelt Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Angewandte Mathematik
Schlagworte Boundary value problem • Calculus • finite difference methods • Fourier series • maximum principles • partial differential equation • Partial differential equations • Partielle Differenzialgleichungen • Reaction-Diffusion Equations • wave equation
ISBN-10 3-540-22551-X / 354022551X
ISBN-13 978-3-540-22551-5 / 9783540225515
Zustand Neuware
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