An Introduction to Numerical Analysis
An Introduction to Numerical Analysis
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.
- Class tested and based on a course taught by the authors at Oxford University
- Motivational and contextual material brings the subject alive
- Can be used as a reference by those working in other fields
Reviews & endorsements
'The book is easy to read. It flows smoothly and I would consider it to be well worth the money and a useful update to the literature.' Mathematics Today
'The book is well written and offers a good level of rigor for the intended readership … good book for mathematics students who come armed with some background in analysis.' Eugene L. Allgower, Colorado State University
'This is an excellent book for introducing undergraduates to the fascinating discipline of numerical analysis. It is the result of many years of lectures held by the authors at the University of Oxford, a fact that explains the evident ability of the book of addressing questions frequently asked by students.' Internationale Mathematische Nachrichten
'This is a very good textbook to introduce mathematics students to numerical analysis … The authors have made a good choice of introductory topics in numerical analysis … The book is very carefully written and can indeed be recommended as a textbook for a course for second or third year mathematics students … It is a pleasure to browse through this book; it is written in a pleasant style and contains many historic references to ancient and modern mathematicians with some details about their lives.' Zentralblatt MATH
'The book is well written and offers a good level of rigor for the intended readership … This is a good book for mathematics students who come armed with some background in analysis. It is carefully written with a good level of rigor.' Eugene L. Allgower, Colorado State University,
Product details
August 2003Paperback
9780521007948
444 pages
226 × 152 × 25 mm
0.853kg
100 b/w illus. 3 colour illus.
Available
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.
