Delta Functions: An Introduction to Generalised Functions

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Horwood Publishing, 2009 - Mathematics - 270 pages
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Delta Functions has now been updated, restructured and modernised into a second edition, to answer specific difficulties typically found by students encountering delta functions for the first time. In particular, the treatment of the Laplace transform has been revised with this in mind. The chapter on Schwartz distributions has been considerably extended and the book is supplemented by a fuller review of Nonstandard Analysis and a survey of alternative infinitesimal treatments of generalised functions.

Dealing with a difficult subject in a simple and straightforward way, the text is readily accessible to a broad audience of scientists, mathematicians and engineers. It can be used as a working manual in its own right, and serves as a preparation for the study of more advanced treatises. Little more than a standard background in calculus is assumed, and attention is focused on techniques, with a liberal selection of worked examples and exercises.

  • Second edition has been updated, restructured and modernised to answer specific difficulties typically found by students encountering delta functions for the first time
  • Attention is focused on techniques, with a liberal selection of worked examples and exercises
  • Readily accessible to a broad audience of scientists, mathematicians and engineers and can be used as a working manual in its own right
 

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Contents

Table of Contents
1
The Dirac Delta Function
26
Properties of the Delta Function
47
Timeinvariant Linear Systems
76
The Laplace Transform
99
Fourier Series and Transforms
128
Other Generalised Functions
154
Introduction to distributions
171
Integration Theory
194
Introduction to N S A
209
Nonstandard Generalised Functions
237
Solutions to Exercises
261
Index
269
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