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Asymptotic Analysis: A Distributional Approach by Ricardo Estrada, Ram P. Kanwal
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About this book :-
Asymptotic Analysis: A Distributional Approach written by
Ricardo Estrada, Ram P. Kanwal.
Asymptotic analysis is an old subject that has found applications in various fields of pure and applied mathematics, physics and engineering. For instance, asymptotic techniques are used to approximate very complicated integral expressions that result from transform analysis. Similarly, the solutions of differential equations can often be computed with great accuracy by taking the sum of a few terms of the divergent series obtained by the asymptotic calculus.
An important feature of the theory of asymptotic expansions is that experience and intuition play an important part in it because particular problems are rather individual in nature. Our aim is to present a systematic and simplified approach to this theory by the use of distributions (generalized functions). The theory of distributions is another important area of applied mathematics, that has also found many applications in mathematics, physics and engineering. It is only recently, however, that the close ties between asymptotic analysis and the theory of distributions have been studied in detail. As it turns out, generalized functions provide a very appropriate framework for asymptotic analysis, where many analytical operations can be performed, and also provide a systematic procedure to assign values to the divergent integrals that often appear in the literature.
The book is suitable for a one semester graduate course in mathematical and physical sciences. We have offered courses inspired by this material at our respective universities. Although the book is based on our own research work, we have attempted to make the material self-contained. With that goal in mind we have incorporated one
on the introduction of classical asymptotic analysis and one
on the basic principles of generalized functions as needed in the sequel.
(Ram P. Kanwal)
Book Detail :-
Title: Asymptotic Analysis: A Distributional Approach
Edition:
Author(s): Ricardo Estrada, Ram P. Kanwal
Publisher: Birkhäuser Boston
Series:
Year: 1994
Pages: 463
Type: PDF
Language: English
ISBN: 978-1-4684-0031-1,978-1-4684-0029-8
Country: US
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About Author :-
The author Ram P. Kanwal, Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania, PA 16802, US.
The author Ricardo Estrada, Escuela de Matematica, Universidad de Costa Rica, 2060 San Jose, Costa Rica.
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Book Contents :-
Asymptotic Analysis: A Distributional Approach written by
Ricardo Estrada, Ram P. Kanwal
cover the following topics.
1. Basic Results in Asymptotics
2. Introduction to the Theory of Distributions
3. A Distributional Theory for Asymptotics Expansion
4. The Asymptotic Expansion of Multidimensional Gernelized Functions
5. The Asymptotic Expansion of Certain Series Considered
6. Series of Dirac Delta Functions
Refrences
Index
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