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Generalized Functions: Theory & Applications by Ram P. Kanwal
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About this book :-
Generalized Functions: Theory & Applications written by
Ram P. Kanwal.
There has recently been a significant increase in the number of topics for which generalized functions have been found to be very effective tools . Familiarity with the basic concepts of this theory has become indispensable for students in applied mathematics, physics, and engineering, and it is becoming increasingly clear that methods based on generalized functions not only help us to solve unsolved problems but also enable us to recover known solutions in a very simple fashion.
This book contains both the theory and applications of generalized functions, with a significant feature being the quantity and variety of applications of this theory. The authors have attempted to furnish a wealth of applications from various physical and mathematical fields of current interest and have tried to make the presentation direct yet informal. Definitions and theorems are stated precisely, but rigor is minimized in favor of comprehension of techniques. Many examples are presented to illustrate the concepts, definitions, and theorems. Except for a few research topics, the mathematical background expected from a student is available in undergraduate courses in advanced calculus, ordinary and partial differential equations, and boundary value problems. Accordingly, most of the material is easily accessible to senior undergraduate and graduate students in mathematical, physical, and engineering sciencs. The chapters that are suitable for a one-semester course are furnished with sets of exercises.
This book will encourage applied mathematicians, scientists, and engineers to make use of the powerful tools of generalized functions.
(Ram P. Kanwal)
Book Detail :-
Title: Generalized Functions: Theory & Applications
Edition:
Author(s): Ram P. Kanwal
Publisher: Birkhäuser Basel
Series:
Year: 2004
Pages: 489
Type: PDF
Language: English
ISBN: 978-0-8176-4343-0,978-0-8176-8174-6
Country: US
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About Author :-
The author Ram P. Kanwal Department of Mathematics, Pennsylvania State University University Park, Pennsylvania, US.
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Book Contents :-
Generalized Functions: Theory & Applications written by
Ram P. Kanwal
cover the following topics.
1. The Dirac Delta Function and Delta Sequences
2. The Schwartz-Sobolev Theory of Distributions
3. Additional Properties of Distributions
4. Distributions Defined by Divergent Integrals
5. Distributional Derivatives of Functions with Jump Discontinuities
6. Tempered Distributions and the Fourier Transform
7. Direct Products and Convolutions of Distributions
8. The Laplace Transform
9. Applications to Ordinary Differential Equations
10. Applications to Partial Differential Equations
11. Applications to Boundary Value Problems
12. Applications to Wave Propagation
13. Interplay Between Generalized Functions and the Theory of Moments
14. Linear Systems
15. Miscellaneous Topics
References
Index
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