An Introduction to Numerical Analysis

Rating:
Summary: A textbook for the theory of numerical analysis
Review: Many people naively believe that with the growing power of symbolic mathematics packages such as Mathematica?, knowledge in numerical analysis is increasingly irrelevant. That is not true, all programmers should have some knowledge of numerical techniques and even power users of a symbolic mathematics package should have some theoretical knowledge in numerical techniques. The packages will perform operations such as polynomial interpolation and at the very least a user should know when to use a specific type.
This book is a solid text in the basics of numerical mathematics, using more of a theoretical background than most. There are a large number of theorem-proof instances, so in that respect, it resembles a math book. The material covered is:

* Solutions of linear equations and systems of linear equations.
* Matrices, eigenvalues and eigenvectors.
* Polynomial interpolation and polynomial approximation.
* Numerical integration.
* Initial value and boundary value problems for ODEs.
* The finite element method.

There are a small number of exercises at the end of each chapter and no solutions are included.
If you are looking for a book to use in a course in numerical analysis where there is an emphasis on the theoretical background, then this one will serve your needs.