Integral transforms and fourier series

Presents the fundamentals of Integral Transforms and Fourier Series with their applications in diverse fields including engineering mathematics. Beginning with the basic ideas, concepts, methods and related theorems of Laplace Transforms and their applications the book elegantly deals in detail the theory of Fourier Series along with application of Drichlet's theorem to Fourier Series.

The book also covers the basic concepts and techniques in Fourier Transform, Fourier Sine and Fourier Cosine transform of a variety of functions in different types of intervals with applications to boundary value problems are the special features of this section of the book. Apart from basic ideas, properties and applications of Z-Transform, the book prepares the readers for applying Transform Calculus to applicable mathematics by introducing basics of other important transforms such as Mellin, Hilbert, Hankel, Weierstrass and Abel's Transform.

Preface	p. v
1 Laplace Transforms with Applications	p. 1.1-1.46
1.1 Introduction	p. 1.1
1.2 Definition	p. 1.1
1.3 Basic Integration Formulas	p. 1.1
1.4 Illustrative Examples on § 1.2	p. 1.3
1.5 Properties of Laplace Transform	p. 1.4
1.6 Laplace Transform of Periodic Functions	p. 1.13
1.7 Unit Step Functions	p. 1.15
1.8 Unit Impulse Function	p. 1.19
1.9 Inverse Laplace Transform	p. 1.21
1.10 Applications of Laplace Transform	p. 1.31
2 Fourier Series	p. 2.1-2.30
2.1 Introduction	p. 2.1
2.2 Definition	p. 2.2
2.3 Some Important Definite Integrals Involving sin x/cos x	p. 2.2
2.4 Illustrative Examples on 2.2	p. 2.3
2.5 Fourier Series of Function Having Point of Discontinuity	p. 2.9
2.6 Illustrative Examples on § 2.5	p. 2.9
2.7 Even and Odd Function: (Cosine and Sine Series)	p. 2.15
2.8 Half Range Series	p. 2.19
2.9 Illustrative Examples on 2.8	p. 2.19
2.10 Extention to arbitrary intervals (Change of Scale)	p. 2.22
3 Fourier Transforms with Applications	p. 3.1-3.37
3.1 Introduction	p. 3.1
3.2 Definition	p. 3.1
3.3 Properties of Fourier Transforms	p. 3.3
3.4 Fourier Integral Theorem	p. 3.5
3.5 Illustrative Examples	p. 3.7
3.6 Convolution and Convolution Theorem for Fourier Transform	p. 3.18
3.7 Parseval's Identify for Fourier Transforms	p. 3.19
3.8 Relation Between Fourier and Laplace Transforms	p. 3.19
3.9 Fourier Transform of the Derivatives of a Function	p. 3.20
3.10 Illustrative Examples on Parseval's Identity	p. 3.22
3.11 Application of Fourier Transforms to Boundary Value Problems	p. 3.23
3.12 Illustrative Examples on Application of Fourier Transforms	p. 3.24
3.13 Some Useful Integrals	p. 3.32
3.14 Table of Fourier Sine and Cosine Transform for Some Standard Functions	p. 3.33
4 Z-Transforms with Applications	p. 4.1-4.32
4.1 Introduction	p. 4.1
4.2 Sequences and Basic Operations on Sequences	p. 4.1
4.3 Z-Transform	p. 4.2
4.4 Properties of Z-Transforms	p. 4.2
4.5 Z-Transform of kf(k)	p. 4.5
4.6 Z-Transform of f(k)/k	p. 4.5
4.7 Initial Value Theorem	p. 4.6
4.8 Final Value Theorem	p. 4.6
4.9 Partial Sum Theorem	p. 4.7
4.10 Convolution Theorem	p. 4.7
4.11 Illustrative Examples	p. 4.8
4.12 Inverse Z-Transform	p. 4.14
4.13 Methods to Find Inverse Z-Transform	p. 4.14
4.14 Application of Z-Transforms	p. 4.22
4.15 Difference Equations and its Solutions	p. 4.22
4.16 Illustrative Examples on 4.14, 4.15	p. 4.24
4.17 Table of Z-Transforms for Some Important Sequences	p. 4.29
5 Hankel and Other Transforms	p. 5.1-5.15
5.1 Introduction	p. 5.1
5.2 The Hankel Transform	p. 5.2
5.3 Illustrative Examples	p. 5.3
5.4 Properties of Hankel Transform	p. 5.6
5.5 Application of Hankel Transform to Boundary Value Problems	p. 5.9
Bibliography	p. B.1
Index	p. I.1
About the Authors	p. A.1

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