An Introduction to Numerical Analysis

by Endre Süli , David F. Mayers

• ISBN13: 9780521007948
• ISBN10: 0521007941
• Format: Paperback
• Copyright: 2003-09-08
• Publisher: Cambridge University Press

Summary

Numerical analysis provides the theoretical foundation for the numerical algorithms we rely on to solve a multitude of computational problems in science. Based on a successful course at Oxford University, this book covers a wide range of such problems ranging from the approximation of functions and integrals to the approximate solution of algebraic, transcendental, differential and integral equations. Throughout the book, particular attention is paid to the essential qualities of a numerical algorithm - stability, accuracy, reliability and efficiency. The authors go further than simply providing recipes for solving computational problems. They carefully analyse the reasons why methods might fail to give accurate answers, or why one method might return an answer in seconds while another would take billions of years. This book is ideal as a text for students in the second year of a university mathematics course. It combines practicality regarding applications with consistently high standards of rigour.

Table of Contents

1. Solution of equations by iteration

2. Solution of systems of linear equations

3. Special matrices

4. Simultaneous nonlinear equations

5. Eigenvalues and eigenvectors of a symmetric matrix

6. Polynomial interpolation

7. Numerical integration - I

8. Polynomial approximation in the 

-norm

9. Approximation in the 2-norm

10. Numerical integration - II

11. Piecewise polynomial approximation

12. Initial Value Problems for ODEs

13. Boundary Value Problems for ODEs

14. The Finite Element Method

Appendix 1. An overview of results from real analysis

Appendix 2. WWW-resources.