Theoretical Numerical Analysis
A Functional Analysis Framework
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Beschreibung
Overall, the book is clearly written, quite pleasant to read, and contains a lot of important material; and the authors have done an excellent job at balancing theoretical developments, interesting examples and exercises, numerical experiments, and bibliographical references.
- R. Glowinski, SIAM Review
Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the clas sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this text book series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Math ematical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs.
This text covers the basics of functional analysis and also some additional topics in numerical analysis. It is suitable for graduate courses in numerical analysis in mathematics, engineering, physics, chemistry, and related departments and is useful for researchers in these areas. It is especially for graduate students in mathematics who wish to work in theoretical numerical analysis and seek a background in the "tools of the trade" covered in this text.
Autor*in
Kendall Atkinson
Themen in »Theoretical Numerical Analysis«
Banach fixed-point theorem Derivative Finite Element Methods calculus differential equation finite element method fixed-point theorem functional analysis numerical analysis numerical methods orthogonal polynomials
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From the reviews:
MATHEMATICAL REVIEWS
"The book starts with two chapters that introduce the reader to functional analysis. In these 89 pages the functional-analytic framework for dealing with theoretical numerical analysis problems is developed from scratch, starting with the definition of a linear space. The authors achieve this remarkable feat by avoiding a formalized framework Lebesgue measure, integration, and distribution theory. Instead they use more standard results on the completion of normal spaces and the unique extension of densely defined bounded linear operators. This is a very interesting approach. Actually these two chapters might form the basis for a functional analysis course in its own right. The rest of the book covers a wealth of topics and might serve as the basis for several graduate courses…The book is well written and accessible to students who have had the usual mathematics undergraduate courses in analysis, linear algebra and numerical analysis. It can be recommended as a textbook for several graduate mathematical courses and also as a reference work for numerical analysts who are interested in the general mathematical aspects of their work."
K.l. Atkinson and W. Han
Theoretical Numerical Analysis A Functional Analysis Framework
"The book is well written and accessible to students who have had the usual mathematics undergraduate courses in analysis, linear algebra and numerical analysis. It can be recommended as a textbook for several graduate mathematical courses and as a reference work for numerical analysts interested in the general mathematical aspects of their work." —AMERICAN MATHEMATICAL SOCIETY
From the reviews of the second edition:
"This is the second, expanded edition of the book published originally in 2001. … The book can be recommended as an introduction to the so-called theoretical numerical analysis … . The text presupposes only the basic undergraduate knowledge of linear algebra, analysis and numerical methods and is thus suitable as a basis for advanced undergraduate and beginning graduate courses. All sections end with exercises, and at the end of each chapter the reader will find useful suggestions for further reading." (Aleksandar Perovic, Zentralblatt MATH, Vol. 1068, 2005)
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