Ebook: Generalized Functions Theory and Technique

The theory of generalized functions is a fundamental part of the toolkit of mathematicians, physicists, and theoretically inclined engineers. It has become increasingly clear that methods based on this theory, also known as the theory of distributions, not only help us to solve previously unsolved problems but also enalble us to recover known solutions in a very simple manner.
This book contains both the theory and applications of generalized functions with a significant feature being the quantity and variety of applications. Definitions and theorems are stated precisely, but rigor is minimized in favor of comprehension of techniques. Most of the material is easily accessible to senior undergraduate and graduate students in mathematical, physical and engineering sciences. The background required is limited to the standard courses in advanced calculus, ordinary and partial differential equations, and boundary value problems. The chapters that are suitable as a one semester course are furnished with sets of exercises.
This edition has been strengthened in many ways. Various new concepts have been added. Some of the new material has been reorganized to improve the logical flow of ideas. And the set of examples has been expanded considerably to make more of the ideas concrete in the reader's eye.

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Content:
Front Matter....Pages i-xii
The Dirac Delta Function and Delta Sequences....Pages 1-17
The Schwartz-Sobolev Theory of Distributions....Pages 18-48
Additional Properties of Distributions....Pages 49-70
Distributions Defined by Divergent Integrals....Pages 71-98
Distributional Derivatives of Functions with Jump Discontinuities....Pages 99-137
Tempered Distributions and the Fourier Transform....Pages 138-172
Direct Products and Convolutions of Distributions....Pages 173-207
The Laplace Transform....Pages 208-218
Applications to Ordinary Differential Equations....Pages 219-255
Applications to Partial Differential Equations....Pages 256-296
Applications to Boundary Value Problems....Pages 297-343
Applications to Wave Propagation....Pages 344-380
Interplay Between Generalized Functions and the Theory of Moments....Pages 381-404
Linear Systems....Pages 405-418
Miscellaneous Topics....Pages 419-448
Back Matter....Pages 449-462

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Content:
Front Matter....Pages i-xii
The Dirac Delta Function and Delta Sequences....Pages 1-17
The Schwartz-Sobolev Theory of Distributions....Pages 18-48
Additional Properties of Distributions....Pages 49-70
Distributions Defined by Divergent Integrals....Pages 71-98
Distributional Derivatives of Functions with Jump Discontinuities....Pages 99-137
Tempered Distributions and the Fourier Transform....Pages 138-172
Direct Products and Convolutions of Distributions....Pages 173-207
The Laplace Transform....Pages 208-218
Applications to Ordinary Differential Equations....Pages 219-255
Applications to Partial Differential Equations....Pages 256-296
Applications to Boundary Value Problems....Pages 297-343
Applications to Wave Propagation....Pages 344-380
Interplay Between Generalized Functions and the Theory of Moments....Pages 381-404
Linear Systems....Pages 405-418
Miscellaneous Topics....Pages 419-448
Back Matter....Pages 449-462
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