UID:
almahu_9949697526402882
Format:
1 online resource (283 p.)
Edition:
2nd ed.
ISBN:
0-85709-935-3
Content:
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 rea
Note:
Includes index.
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Cover; ABOUT THE AUTHOR; DELTA FUNCTIONS:An Introduction to GeneralisedFunctions; Copyright; Preface; Contents; 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 2The 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 OFFUNCTION THEORYDELTA; 2.6 HISTORICAL NOTE
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Chapter 3Properties of the DeltaFunction3.1 THE DELTA FUNCTION AS A FUNCTIONAL; 3.2 SUMS AND PRODUCTS; 3.3 DIFFERENTIATION; 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
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5.4 NOTE ON INVERSIONChapter 6 Fourier Series and Transforms; 6.1 FOURIER SERIES; 6.2 GENERALISED FOURIER SERIES; 6.3 FOURIER TRANSFORMS; 6.4 GENERALISED FOURIER TRANSFORMS; Chapter 7Other Generalised Functions; 7.1 FRACTIONAL CALCULUS; 7.2 HADAMARD FINITE PART; 7.3 PSEUDO-FUNCTIONS; Chapter 8Introduction to distributions; 8.1 TEST FUNCTIONS; 8.2 FUNCTIONALS AND DISTRIBUTIONS; 8.3 CALCULUS OF DISTRIBUTIONS; 8.4 GENERAL SCHWARTZ DISTRIBUTIONS; Chapter 9Integration Theory; 9.1 RIEMANN-STIELTJES INTEGRALS; 9.2 EXTENSION OF THE ELEMENTARY INTEGRAL; 9.3 THE LEBESGUE AND RIEMANNINTEGRALS
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Chapter 10Introduction to N .S.A10.1 A NONSTANDARD NUMBER SYSTEM; 10.2 NONSTANDARD EXTENSIONS; 10.3 ELEMENTARY ANALYSIS; 10.4 INTERNAL OBJECTS; Chapter 11Nonstandard GeneralisedFunctions; 11.1 NONSTANDARD δ-FUNCTIONS; 11.2 PRE-DELTA FUNCTIONS; 11.3 PERIODIC DELTA FUNCTIONS; 11.4 N.S.A. AND DISTRIBUTIONS; Solutions to Exercises; Index
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English
Additional Edition:
ISBN 1-904275-39-7
Language:
English
