This book introduces students with diverse backgrounds to various types of mathematical analysis that are commonly needed in scientific computing. The subject of numerical analysis is treated from a mathematical point of view, offering a complete analysis of methods for scientific computing with appropriate motivations and careful proofs. In an engaging and informal style, the authors demonstrate that many computational procedures and intriguing questions of computer science arise from theorems and proofs. Algorithms are presented in pseudocode, so that students can immediately write computer programs in standard languages or use interactive mathematical software packages. This book occasionally touches upon more advanced topics that are not usually contained in standard textbooks at this level.
 
Table of content 
 
Cover
Title page
Copyright
Dedication
Contents
Preface
Numerical analysis: What is it?
1. Mathematical preliminaries
2. Computer arithmetic
3. Solution of nonlinear equations
4. Solving systems of linear equations
5. Selected topics in numerical linear algebra
6. Approximating functions
7. Numerical differentiation and integration
8. Numerical solution of ordinary differential equations
9. Numerical solution of partial differential equations
10. Linear programming and related topics
11. Optimization
Appendix A. An Overview of mathematical software
Bibliography
Index
Back Cover