Elements of Scientific Computing

Aslak Tveito, Hans Petter Langtangen, Bjørn Frederik Nielsen, Xing Cai

Springer Science & Business Media, Sep 24, 2010 - Mathematics - 468 pages

Science used to be experiments and theory, now it is experiments, theory and computations. The computational approach to understanding nature and technology is currently flowering in many fields such as physics, geophysics, astrophysics, chemistry, biology, and most engineering disciplines. This book is a gentle introduction to such computational methods where the techniques are explained through examples. It is our goal to teach principles and ideas that carry over from field to field. You will learn basic methods and how to implement them. In order to gain the most from this text, you will need prior knowledge of calculus, basic linear algebra and elementary programming.

Contents

• 1 Computing Integrals: 1
• The First Steps: 30
• 3 Systems of Ordinary Differential Equations: 75
• 4 Nonlinear Algebraic Equations: 99
• 5 The Method of Least Squares: 146
• 6 About Scientific Software: 195
• 7 The Diffusion Equation: 273
• 8 Analysis of the Diffusion Equation: 358
• 9 Parameter Estimation and Inverse Problems: 411
• 10 A Glimpse of Parallel Computing: 422
• References: 455
• Index: 457
• Editorial Policy: 460
• Series Editors: 461
• Texts in Computational Scienceand Engineering: 462

About the author

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.

Bibliographic information

• Title: Elements of Scientific Computing; Volume 7 of Texts in Computational Science and Engineering
• Authors: Aslak Tveito, Hans Petter Langtangen, Bjørn Frederik Nielsen, Xing Cai
• Edition: illustrated
• Publisher: Springer Science & Business Media, 2010
• ISBN: 3642112994, 9783642112997
• Length: 468 pages
• Subjects: Computers / Artificial Intelligence / General; Computers / Computer Science; Mathematics / Applied; Mathematics / Counting & Numeration; Mathematics / Numerical Analysis; Mathematics / Probability & Statistics / Stochastic Processes; Science / Life Sciences / Biology; Science / Life Sciences / General; Science / Physics / Mathematical & Computational; Technology & Engineering / Engineering (General)