Mathematical Principles for
Scientific Computing and Visualization

by Gerald Farin & Dianne Hansford

published by A K Peters, Ltd., October 2008

ISBN: 978-1-56881-321-9

Mathematical Principles for Scientific Computing and Visualization is intended for students and researchers in sciences-related areas, e.g., biology, geography, or psychology. In the course of their research pursuits, they will be exposed to various packages for solving their problems, be it from statistics, applied math, or scientific visualization in addition to domain-specific software. This book is intended as a guide to understanding what is underlying the more general software packages. Na´ve and uneducated use might produce meaningless or erroneous results.

Hence this text is not a traditional introduction to the mathematics of scientific computation. Instead it describes the principles behind the major methods in a way that is accessible to a large part of the scientific community. Many examples are included (in favor of any proofs), but not only those which actually work - it is often more important to understand and learn from failed attempts.

The book provides a copious number of illustrations, and not only in the ``visualization" part. The reader is lead to understand many concepts by graphical examples. All illustrations are available on this web site, as well as the Mathematica code used for running the examples in the book. There is also a complete set of classroom presentations. (These material may be found under teaching materials and downloads.)




Brief Table of Contents

1. Introduction
2. Computational Basics

3. Coordinate Systems
4. Background: Numerical Linear Algebra
5. Solving Linear Systems
6. Eigen-problems
7. Background: Numerical Calculus
8. Data Fitting
9. Computing Dynamic Processes
10. Finding Roots
11. Computing with Multivariate Functions
12. Visualizing Empirical Data
13. Facets
14. Visualizing Scalar Data over 2D Data
15. Volume Visualization
16. Background: Computer Graphics



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