Professor Aslak Tveito is the managing director of Simula Research Laboratory. His research is focused on computing the electrical activity in the heart. Tveito is the co-author of more than 60 papers published in international peer-reviewed journals, and one textbook introducing partial differential equations. Tveito has also edited four books published internationally. Professor Hans Petter Langtangen is the director of Center for Biomedical Computing, a Norwegian Center of Excellence at Simula Research Laboratory, and a professor of computer science at the University of Oslo. His research concerns numerical methods and software tools for continuum mechanical problems. Langtangen has published more than 40 journal papers, and more than 50 peer-reviewed contributions to conference proceedings and books. He is the author of three textbooks and an a co-editor of three books. Langtangen has been an active developer of open source and commercial software systems for computational sciences. He is a member of the European Academy of Sciences and serves on the editorial board of five leading international journals. Dr. Nielsen is a research scientist at Simula Research Laboratory where he investigates whether it is possible to compute the position and size of heart infarctions from ECG recordings. He has published a number of papers on computational mathematics and during his years at Norwegian Computing Center he solved many scientific computing problems for the Norwegian oil industry. The research interests of Professor Xing Cai center around parallel numerical methods and software for solving partial differential equations. He has more than 50 peer-reviewed publications in international journals and conference proceedings.

Leicht nachvollziehbar führt das Lehrbuch in Standardthemen wie Trennung der Variablen, Fourier Analysis und Maximumprinzipien ein. Es stellt numerische Verfahren parallel zur klassischen Theorie vor, veranschaulicht die Eigenschaften von Differentialgleichungen anhand numerischer Experimente und entwickelt die Theorie der finiten Differentialapproximationen. Die Einführung numerischer Verfahren zeigt die Bedeutung des Rechnens bei partiellen Differentialgleichungen und illustriert die Interaktion zwischen mathematischer Theorie und der Entwicklung numerischer Verfahren.

1 Das Problemfeld.- 2 Zweipunkt-Randwertaufgaben.- 3 Die Wärmeleitungsgleichung.- 4 Finite Differenzen für die Wärmeleitungsgleichung.- 5 Die Wellengleichung.- 6 Maximumprinzipien.- 7 Die Poisson-Gleichung im Zweidimensionalen Raum.- 8 Orthogonalität und allgemeine Fourierreihen.- 9 Konvergenz von Fourierreihen.- 10 Noch einmal die Wärmeleitungsgleichung.- 11 Reaktions-Diffusionsgleichungen.- 12 Anwendungen der Fouriertransformation.