An Introduction to Numerical Analysis
Seiten
2003
Cambridge University Press (Verlag)
978-0-521-00794-8 (ISBN)
Cambridge University Press (Verlag)
978-0-521-00794-8 (ISBN)
Based on a successful course at Oxford University, this book gives an authoritative introduction to numerical analysis. It 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. Numerous exercises are provided.
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.
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.
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.
| Erscheint lt. Verlag | 28.8.2003 |
|---|---|
| Zusatzinfo | 3 Plates, color; 100 Line drawings, unspecified |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 152 x 226 mm |
| Gewicht | 853 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| ISBN-10 | 0-521-00794-1 / 0521007941 |
| ISBN-13 | 978-0-521-00794-8 / 9780521007948 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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