Rainer Kress (auth.)0387984089, 9780387984087
No applied mathematician can be properly trained without some basic un derstanding ofnumerical methods, Le., numerical analysis. And no scientist and engineer should be using a package program for numerical computa tions without understanding the program’s purpose and its limitations. This book is an attempt to provide some of the required knowledge and understanding. It is written in a spirit that considers numerical analysis not merely as a tool for solving applied problems but also as a challenging and rewarding part of mathematics. The main goal is to provide insight into numerical analysis rather than merely to provide numerical recipes. The book evolved from the courses on numerical analysis I have taught since 1971 at the University ofGottingen and may be viewed as a successor of an earlier version jointly written with Bruno Brosowski [10] in 1974. It aims at presenting the basic ideas of numerical analysis in a style as concise as possible. Its volume is scaled to a one-year course, i.e., a two-semester course, addressing second-yearstudents at a German university or advanced undergraduate or first-year graduate students at an American university. |
Table of contents :
Front Matter….Pages i-xii
Introduction….Pages 1-4
Linear Systems….Pages 5-24
Basic Functional Analysis….Pages 25-52
Iterative Methods for Linear Systems….Pages 53-76
Ill-Conditioned Linear Systems….Pages 77-92
Iterative Methods for Nonlinear Systems….Pages 93-118
Matrix Eigenvalue Problems….Pages 119-150
Interpolation….Pages 151-188
Numerical Integration….Pages 189-224
Initial Value Problems….Pages 225-256
Boundary Value Problems….Pages 257-286
Integral Equations….Pages 287-316
Back Matter….Pages 317-328 |
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