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Methods of Complex analysis in Partial Differential Equations with Applications by Manfred Kracht, Erwin Kreyszig

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Methods of Complex analysis in Partial Differential Equations with Applications written by Manfred Kracht, Erwin Kreyszig .
This book is devoted to the development of complex function theoretic methods in partial differential equations and to the study of the analytic behavior of solutions. The main purpose of the book is the presentation of some basic facts and recent results, emphasizing the method of integral operators
These methods of applying concepts and results of complex analysis in the study of partial differential equations has become a large field of its own. Indeed, the number of papers in this field and its application to fluid flow, elasticity problems, quantum mechanics, and other areas is growing rapidly, and these results are widely scattered throughout many journals. Since, for the most part, these reports concentrate only on certain aspects of the general theory, and many important new results have not yet been included in any book at all, we shall pay particular attention to that progress during the last years as well as to the unification of various approaches and results, thereby exhibiting common features and comparing advantages and limitations of different methods.
(Manfred Kracht, Erwin Kreyszig)

Book Detail :-
Title: Methods of Complex Analysis in Partial Differential Equations with Applications
Edition:
Author(s): Manfred Kracht, Erwin Kreyszig
Publisher: Wiley
Series: Canadian Mathematical Society series of monographs and advanced texts
Year: 1988
Pages: 404
Type: PDF
Language: English
ISBN: 0471830917,9780471830917
Country: Canada
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About Author :- Erwin O. Kreyszig (1922–2008) was a German Canadian applied mathematician and the Professor of Mathematics at Carleton University in Ottawa, Ontario, Canada. He was a pioneer in the field of applied mathematics: non-wave replicating linear systems. He was also a distinguished author, having written the textbook Advanced Engineering Mathematics, the leading textbook for civil, mechanical, electrical, and chemical engineering undergraduate engineering mathematics.
Kreyszig received his Ph.D. degree in 1949 at the University of Darmstadt under the supervision of Alwin Walther.
Manfred Kracht, University of Diisseldorf, Dksseldorf, Germany.

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Methods of Complex analysis in Partial Differential Equations with Applications written by Manfred Kracht, Erwin Kreyszig cover the following topics.
1. Introduction
2. Bergman Operators. General Theory
3. Related Ideas and Operators,
4. Polynomial Kernels: Existence and Construction
5. Further Closed-Form Kernels
6. Riemann- Vekua Representation and Further Methods Related to Bergman Kernels
7. Determination of Riemann Functions
8. Coefficient Problem and Singularities of Solutions
9. Approximation of Solutions
10. Value Distribution Theory of Solutions
11. Applications of Class P Operators. Function Theory of the Bauer-Peschl Equation
12. Application to Compressible Fluid Flow
13. Integral Operators Applied to Transonic Flow Tricomi Equation
Additional References,
Bibliography
Symbol Index
Author Index
Subject Index


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