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# Numerical Analysis by Rainer Kress, F. W. Gehring

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Numerical Analysis written by Rainer Kress, F. W. Gehring .
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 of Gottingen 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-year students at a German university or advanced undergraduate or first-year graduate students at an American university.
In order to make the book accessible not only to mathematicians but also to scientists and engineers, I have planned it to be as self-contained as possible. As prerequisites it requires only a solid foundation in differential and integral calculus and in linear algebra as well as an enthusiasm to see these fundamental and powerful tools in action for solving applied problems.
A short presentation of some basic functional analysis is provided in the book to the extent required for a modern presentation of numerical analysis and a deeper understanding of the subject.

Book Detail :-
Title: Numerical Analysis
Edition:
Author(s): Rainer Kress, F. W. Gehring
Publisher: Springer
Year: 1998
Pages: 340
Type: PDF
Language: English
ISBN: 0387984089,9780387984087
Country: Germany
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The author Rainer Kress was born 1941 in Kassel, Germany. After studying mathematics and physics at the Technische Hochschule Darmstadt he received his doctorate in 1968 and his habilitation in 1969. From 1970 until 1971 he served as a research fellow at the Max-Planck-Institut for Physics and Astrophysics in Munich. He has been a full professor of numerical and applied mathematics in Göttingen since 1971. At the University of Göttingen, from 1974 until 1975 he served as chairman of the Fachbereich Mathematik, from 1978 until 1981 as dean of the Mathematisch Naturwissenschaftliche Fakultät, and from 1993 until 1995 as vice president. Since 1995 he is a member of the Göttingen Academy of Sciences. In 1975 he declined an offer for a full professorship at the Technical University in Berlin. Since 2010 he is professor emeritus.
The main research interests of Rainer Kress are in integral equations with emphasis on numerical methods and in direct and inverse boundary value problems in scattering theory. He is on the editorial board of two international journals in the above areas, that is, Journal of Integral Equations and Applications, and Journal of Inverse and Ill-posed Problems. He has resigned from the editorial board of Inverse Problems, Mathematical Methods in the Applied Sciences, and SIAM Journal on Numerical Analysis. He is author of five books. The second and forth book were jointly written with David Colton from the University of Delaware, the second book was translated into Russian by Mir (Moscow, 1987), and authorized reprints of the third and fifth book were made in China. Since 1971 he was adviser of 31 PhD students and around 100 diplom students.
Rainer Kress had appointments as a visiting professor at the University of Strathclyde in Scotland, the University of Delaware in the US and the University of New South Wales in Australia. Current and active international contacts are with the University of Delaware (USA), the Texas A&M University (USA), the Rutgers University (USA), Inria-Rocquencourt (France), and the Izmir Institute of Technology (Turkey). He was co-organizer of the annual GAMM meetings 1975 and 2000 in Göttingen and of five workshops at the mathematical research institute in Oberwolfach between 1980 and 2000. Since around 1995 he was on the organizing committee of more than 10 international conferences on inverse problems.

The author Frederick William Gehring was an American mathematician who born in 7 August 1925. Gehring graduated from University High School in 1943. He instead enrolled in the V-12 Navy College Training Program at the University of Michigan where he earned a BE in electrical engineering and a BA in mathematics in addition to completing various other Navy courses. He obtained a Master's degree in mathematics. In 1949 Gehring went to the University of Cambridge to study mathematics. Gehring received his Ph.D. in mathematics in 1952.
Gehring served as a Benjamin Peirce instructor at Harvard University for three years after completing his doctoral work at the University of Cambridge. In 1955 he assume a post on the faculty of the Department of Mathematics at the University of Michigan where he worked until he retired at age 70. During this time he supervised 29 Ph.D. students, six of whom are women, as well as 40 postdoctoral visitors.[3] He also served as Chairman of the department on three separate occasions, serving for a total of eight years. He worked in the area of complex analysis. In 2006, awarded the American Mathematical Society Steele Prize for Lifetime Achievement.

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• Download PDF Integral Equation Methods in Scattering Theory by David Colton, Rainer Kress

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Book Contents :-
Numerical Analysis written by Rainer Kress, F. W. Gehring cover the following topics.
1. Introduction
2. Linear Systems
3. Basic Functional Analysis
4. Iterative Methods for Linear Systems
5. Ill-Conditioned Linear Systems
6. Iterative Methods for Nonlinear Systems
7. Matrix Eigenvalue Problems
8. Interpolation
9. Numerical Integration
10. Initial Value Problems
11. Boundary Value Problems
12. Integral Equations

Problems .
References
Index

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