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" Integral transforms and their applications "
Lokenath Debnath, Dambaru Bhatta.
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BL
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754777
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b574739
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| Main Entry
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Lokenath Debnath, Dambaru Bhatta.
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Integral transforms and their applications\ Lokenath Debnath, Dambaru Bhatta.
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| Edition Statement
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Third edition
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| Publication Statement
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Boca Raton : Taylor & Francis, 2015
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| ISBN
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1482223589
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: 9781482223583
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| Notes
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A CRC title.
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| Contents
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Machine generated contents note: 1.1. Brief Historical Introduction --; 1.2. Fourier Series and Fourier Transforms --; 1.3. Gabor Transforms --; 1.4. Basic Concepts and Definitions --; 2.1. Introduction --; 2.2. Fourier Integral Formulas --; 2.3. Definition of the Fourier Transform and Examples --; 2.4. Fourier Transforms of Generalized Functions --; 2.5. Basic Properties of Fourier Transforms --; 2.6. Poisson's Summation Formula --; 2.7. Shannon Sampling Theorem --; 2.8. Gibbs Phenomenon --; 2.9. Heisenberg's Uncertainty Principle --; 2.10. Applications of Fourier Transforms to Ordinary Differential Equations --; 2.11. Solutions of Integral Equations --; 2.12. Solutions of Partial Differential Equations --; 2.13. Fourier Cosine and Sine Transforms with Examples --; 2.14. Properties of Fourier Cosine and Sine Transforms --; 2.15. Applications of Fourier Cosine and Sine Transforms to Partial Differential Equations --; 2.16. Evaluation of Definite Integrals --; 2.17. Applications of Fourier Transforms in Mathematical Statistics --; 2.18. Multiple Fourier Transforms and Their Applications --; 2.19. Exercises --; 3.1. Introduction --; 3.2. Definition of the Laplace Transform and Examples --; 3.3. Existence Conditions for the Laplace Transform --; 3.4. Basic Properties of Laplace Transforms --; 3.5. Convolution Theorem and Properties of Convolution --; 3.6. Differentiation and Integration of Laplace Transforms --; 3.7. Inverse Laplace Transform and Examples --; 3.8. Tauberian Theorems and Watson's Lemma --; 3.9. Exercises --; 4.1. Introduction --; 4.2. Solutions of Ordinary Differential Equations --; 4.3. Partial Differential Equations, Initial and Boundary Value Problems --; 4.4. Solutions of Integral Equations --; 4.5. Solutions of Boundary Value Problems --; 4.6. Evaluation of Definite Integrals --; 4.7. Solutions of Difference and Differential-Difference Equations --; 4.8. Applications of the Joint Laplace and Fourier Transform --; 4.9. Summation of Infinite Series --; 4.10. Transfer Function and Impulse Response Function of a Linear System --; 4.11. Double Laplace Transform, Functional and Partial Differential Equations --; 4.12. Exercises --; 5.1. Introduction --; 5.2. Historical Comments --; 5.3. Fractional Derivatives and Integrals --; 5.4. Applications of Fractional Calculus --; 5.5. Exercises --; 6.1. Introduction --; 6.2. Laplace Transforms of Fractional Integrals and Fractional Derivatives --; 6.3. Fractional Ordinary Differential Equations --; 6.4. Fractional Integral Equations --; 6.5. Initial Value Problems for Fractional Differential Equations --; 6.6. Green's Functions of Fractional Differential Equations --; 6.7. Fractional Partial Differential Equations --; 6.8. Exercises --; 7.1. Introduction --; 7.2. Hankel Transform and Examples --; 7.3. Operational Properties of the Hankel Transform --; 7.4. Applications of Hankel Transforms to Partial Differential Equations --; 7.5. Exercises --; 8.1. Introduction --; 8.2. Definition of the Mellin Transform and Examples --; 8.3. Basic Operational Properties of Mellin Transforms --; 8.4. Applications of Mellin Transforms --; 8.5. Mellin Transforms of the Weyl Fractional Integral and the Weyl Fractional Derivative --; 8.6. Application of Mellin Transforms to Summation of Series --; 8.7. Generalized Mellin Transforms --; 8.8. Exercises --; 9.1. Introduction --; 9.2. Definition of the Hilbert Transform and Examples --; 9.3. Basic Properties of Hilbert Transforms --; 9.4. Hilbert Transforms in the Complex Plane --; 9.5. Applications of Hilbert Transforms --; 9.6. Asymptotic Expansions of One-Sided Hilbert Transforms --; 9.7. Definition of the Stieltjes Transform and Examples --; 9.8. Basic Operational Properties of Stieltjes Transforms --; 9.9. Inversion Theorems for Stieltjes Transforms --; 9.10. Applications of Stieltjes Transforms --; 9.11. Generalized Stieltjes Transform --; 9.12. Basic Properties of the Generalized Stieltjes Transform --; 9.13. Exercises --; 10.1. Introduction --; 10.2. Definitions of the Finite Fourier Sine and Cosine Transforms and Examples --; 10.3. Basic Properties of Finite Fourier Sine and Cosine Transforms --; 10.4. Applications of Finite Fourier Sine and Cosine Transforms --; 10.5. Multiple Finite Fourier Transforms and Their Applications --; 10.6. Exercises --; 11.1. Introduction --; 11.2. Definition of the Finite Laplace Transform and Examples --; 11.3. Basic Operational Properties of the Finite Laplace Transform --; 11.4. Applications of Finite Laplace Transforms --; 11.5. Tauberian Theorems --; 11.6. Exercises --; 12.1. Introduction --; 12.2. Dynamic Linear Systems and Impulse Response --; 12.3. Definition of the Z Transform and Examples --; 12.4. Basic Operational Properties of Z Transforms --; 12.5. Inverse Z Transform and Examples --; 12.6. Applications of Z Transforms to Finite Difference Equations --; 12.7. Summation of Infinite Series --; 12.8. Exercises --; 13.1. Introduction --; 13.2. Definition of the Finite Hankel Transform and Examples --; 13.3. Basic Operational Properties --; 13.4. Applications of Finite Hankel Transforms --; 13.5. Exercises --; 14.1. Introduction --; 14.2. Definition of the Legendre Transform and Examples --; 14.3. Basic Operational Properties of Legendre Transforms --; 14.4. Applications of Legendre Transforms to Boundary Value Problems --; 14.5. Exercises --; 15.1. Introduction --; 15.2. Definition of the Jacobi Transform and Examples --; 15.3. Basic Operational Properties --; 15.4. Applications of Jacobi Transforms to the Generalized Heat Conduction Problem --; 15.5. Gegenbauer Transform and Its Basic Operational Properties --; 15.6. Application of the Gegenbauer Transform --; 16.1. Introduction --; 16.2. Definition of the Laguerre Transform and Examples --; 16.3. Basic Operational Properties --; 16.4. Applications of Laguerre Transforms --; 16.5. Exercises --; 17.1. Introduction --; 17.2. Definition of the Hermite Transform and Examples --; 17.3. Basic Operational Properties --; 17.4. Exercises --; 18.1. Introduction --; 18.2. Radon Transform --; 18.3. Properties of the Radon Transform --; 18.4. Radon Transform of Derivatives --; 18.5. Derivatives of the Radon Transform --; 18.6. Convolution Theorem for the Radon Transform --; 18.7. Inverse of the Radon Transform and the Parseval Relation --; 18.8. Applications of the Radon Transform --; 18.9. Exercises --; 19.1. Brief Historical Remarks --; 19.2. Continuous Wavelet Transforms --; 19.3. Discrete Wavelet Transform --; 19.4. Examples of Orthonormal Wavelets --; 19.5. Exercises --; A-1. Gamma, Beta, and Error Functions --; A-2. Bessel and Airy Functions --; A-3. Legendre and Associated Legendre Functions --; A-4. Jacobi and Gegenbauer Polynomials --; A-5. Laguerre and Associated Laguerre Functions --; A-6. Hermite Polynomials and Weber-Hermite Functions --; A-7. Mittag-Leffler Function --; B-1. Fourier Transforms --; B-2. Fourier Cosine Transforms --; B-3. Fourier Sine Transforms --; B-4. Laplace Transforms --; B-5. Hankel Transforms --; B-6. Mellin Transforms --; B-7. Hilbert Transforms --; B-8. Stieltjes Transforms --; B-9. Finite Fourier Cosine Transforms --; B-10. Finite Fourier Sine Transforms --; B-11. Finite Laplace Transforms --; B-12. Z Transforms --; B-13. Finite Hankel Transforms --; 2.19. Exercises --; 3.9. Exercises --; 4.12. Exercises --; 6.8. Exercises --; 7.5. Exercises --; 8.8. Exercises --; 9.13. Exercises --; 10.6. Exercises --; 11.6. Exercises --; 12.8. Exercises --; 13.5. Exercises --; 16.5. Exercises --; 17.4. Exercises --; 18.9. Exercises --; 19.5. Exercises.
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| Subject
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Integral transforms.
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| Subject
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Mathematics -- Textbooks.
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| Subject
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Mathematics.
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| LC Classification
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QA432.L654 2015
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| Added Entry
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Dambaru Bhatta
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Lokenath Debnath
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