An Introduction to Numerical Analysis (+Solutions to Exercises) - ISBN:0521007941

An Introduction to Numerical Analysis (+Solutions to Exercises)

Date: 08 May 2011, 00:23

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This textbook is written primarily for undergraduate mathematicians and also appeals to students working at an advanced level in other disciplines. The text begins with a clear motivation for the study of numerical analysis based on real-world problems. The authors then develop the necessary machinery including iteration, interpolation, boundary-value problems and finite elements. Throughout, the authors keep an eye on the analytical basis for the work and add historical notes on the development of the subject. There are numerous exercises for students.
A textbook for the theory of numerical analysis.
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.
Review
"This book is a solid text in the basics of numerical mathematics, using more of a theoretical background than most. 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." Journal of Recreational Mathematics
"carefully written with a good level of rigor" SIAM Review
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