Ebook: Numerical Analysis

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.

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This volume is intended as an introduction into numerical analysis for students in mathematics, physics, and engineering. Instead of attempting to exhaustively cover all parts of numerical analysis, the goal is to guide the reader towards the basic ideas and general principles by way of considering main and important numerical methods. Given the rapid development of numerical algorithms, a reasonable introduction to numerical analysis has to confine itself to presenting a solid foundation by restricting the presentation to the basic principles and procedures.