Description

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.

Key Features

  • 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

Readership

Scientists, mathematicians, and engineers

Table of Contents

  • About the Author
  • Preface
  • Chapter 1: Results from Elementary Analysis
    • 1.1 THE REAL NUMBER SYSTEM
    • 1.2 FUNCTIONS
    • 1.3 CONTINUITY
    • 1.4 DIFFERENTIABILITY
    • 1.5 TAYLOR’S THEOREM
    • 1.6 INTEGRATION
    • 1.7 IMPROPER INTEGRALS
    • 1.8 UNIFORM CONVERGENCE
    • 1.9 DIFFERENTIATING INTEGRALS
  • Chapter 2: The Dirac Delta Function
    • 2.1 THE UNIT STEP FUNCTION
    • 2.2 DERIVATIVE OF THE UNIT STEP FUNCTION
    • 2.3 THE DELTA FUNCTION AS A LIMIT
    • 2.4 STIELTJES INTEGRALS
    • 2.5 DEVELOPMENTS OF DELTA FUNCTION THEORY
    • 2.6 HISTORICAL NOTE
  • Chapter 3: Properties of the Delta Function
    • 3.1 THE DELTA FUNCTION AS A FUNCTIONAL
    • 3.2 SUMS AND PRODUCTS
    • Exercises I
    • 3.3 DIFFERENTIATION
    • Exercises II
    • 3.4 DERIVATIVES OF THE DELTA FUNCTION
    • 3.5 POINTWISE DESCRIPTION OF δ′(t)
    • 3.6 INTEGRATION OF THE DELTA FUNCTION
    • 3.7 CHANGE OF VARIABLE
  • Chapter 4: Time-invariant Linear Systems
    • 4.1 SYSTEMS AND OPERATORS
    • 4.2 STEP RESPONSE AND IMPULSE RESPONSE
    • 4.3 CONVOLUTION
    • 4.4 IMPULSE RESPONSE FUNCTIONS
    • 4.5 TRANSFER FUNCTION
  • Chapter 5: The Laplace Transform
    • 5.1 THE CLASSICAL LAPLACE TRANSFORM
    • 5.2 LAPLACE TRANSFORMS OF DELTA FUNCTIONS
    • 5.3 COMPUTATION OF LAPLACE TRANSFORMS
    • 5.4 NOTE ON INVERSION
  • Chapter 6: Fourier Series and Transforms
    • 6.1 FOURIER SERIES
    • 6.2 GENERALISED FOURIER SERIES
    • 6.3 FOURIER TRANSFORMS
    • 6.4 GENERALISED FOURIER TRANSFORMS
  • Chapter 7: Other Generalised Functions
    • 7.1 FRACTIONAL CALCULUS
    • 7.2 HADAMARD FINITE PART
    • 7.3 PSEUDO-FUNCTIONS
  • Chapter 8: Introduction to di

Details

No. of pages:
280
Language:
English
Copyright:
© 2009
Published:
Imprint:
Woodhead Publishing
Electronic ISBN:
9780857099358
Print ISBN:
9781904275398

About the author

Reviews

I find this a good book to teach from and the students can actually read it., Professor H. Westcott Vayo, University of Toledo, USA. (Review of the first edition)