Integral Transforms for Engineers

Author(s): Larry C. Andrews, Bhimsen K. Shivamoggi

Published: 1999

https://doi.org/10.1117/3.339204

PDF ISBN: 9780819478481 | Print ISBN: 9780819432322

DESCRIPTION

Integral transform methods provide effective ways to solve a variety of problems arising in the engineering, optical, and physical sciences. Suitable as a self-study for practicing engineers and applied mathematicians and as a textbook in graduate-level courses in optics, engineering sciences, physics, and mathematics.

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Front Matter

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CHAPTER 1.

Special Functions

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1.1 Introduction
1.2 The Gamma Function
1.3 The Error Function and Related Functions
1.4 Bessel Functions
1.5 Useful Engineering Functions

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CHAPTER 2.

Fourier Integrals and Fourier Transforms

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2.1 Introduction
2.2 Fourier Integral Representations
2.3 Proof of the Fourier Integral Theorem
2.4 Fourier Transform Pairs
2.5 Properties of the Fourier Transform
2.6 Transforms of More Complicated Functions
2.7 The Convolution Integrals of Fourier
2.8 Transforms Involving Generalized Functions
2.9 Hilbert Transforms
2.10 Additional Topics

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CHAPTER 3.

Applications Involving Fourier Transforms

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3.1 Introduction
3.2 Boundary Value Problems
3.3 Heat Conduction in Solids
3.4 Mechanical Vibrations
3.5 Potential Theory
3.6 Hydrodynamics
3.7 Elasticity in Two Dimensions
3.8 Probability and Statistics

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CHAPTER 4.

The Laplace Transform

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4.1 Introduction
4.2 The Transforms of Some Typical Functions
4.3 Basic Operational Properties
4.4 Transforms of More Complicated Functions
4.5 The Inverse Laplace Transform
4.6 Complex Inversion Formula
4.7 Additional Topics

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CHAPTER 5.

Applications Involving Laplace Transforms

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5.1 Introduction
5.2 Evaluating Integrals
5.3 Solutions of ODEs
5.4 Solutions of PDEs
5.5 Linear Integral Equations

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CHAPTER 6.

The Mellin Transform

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6.1 Introduction
6.2 Evaluation of Mellin Transforms
6,3 Complex Variable Methods
6.4 Applications
6.5 Table of Mellin Transforms

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CHAPTER 7.

The Hankel Transform

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7.1 Introduction
7.2 Evaluation of Hankel Transforms
7.3 Applications
7.4 Table of Hankel Transforms

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CHAPTER 8.

Finite Transforms

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8.1 Introduction
8.2 Finite Fourier Transforms
8.3 Sturm—Liouville Transforms
8.4 Finite Hankel Transform

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CHAPTER 9.

Discrete Transforms

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9.1 Introduction
9.2 Discrete Fourier Transform
9.3 The Z Transform
9.4 Difference Equations
9.5 Table of Z Transforms

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Bibliography

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Appendix A Review of Complex Variables

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Appendix B Table of Fourier Transforms

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Appendix C Table of Laplace Transforms

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Back Matter

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