Integral equations and integral transforms

Integral equations and integral transforms Sudeshna Banerjea, Birendra Nath Mandal.

This comprehensive textbook on linear integral equations and integral transforms is aimed at senior undergraduate and graduate students of mathematics and physics. The book covers a range of topics including Volterra and Fredholm integral equations, the second kind of integral equations with symmetr...

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Bibliographic Details
Main Authors: Banerjea, Sudeshna (Author), Mandal, Birendra Nath (Author)
Format: eBook
Language:English
Published: Singapore : Springer, 2023.
Subjects:
Integral equations.
Integral transforms.
Integral equations
Integral transforms
Online Access:Click for online access
Table of Contents:
  • Intro
  • Preface
  • Contents
  • About the Authors
  • Part I Integral Equations
  • 1 Integral Equations: An Introduction
  • 1.1 Introduction
  • 1.1.1 What is an Integral Equation?
  • 1.1.2 Classifications of Integral Equations
  • 1.2 Occurrence of Integral Equations
  • 1.2.1 Occurrence of Volterra Integral Equations
  • 1.2.2 Occurrence of Fredholm Integral Equations
  • References
  • 2 Fredholm Integral Equation of the Second Kind with Degenerate Kernel
  • 2.1 Integral Equation with Degenerate Kernel
  • 2.2 Homogeneous Equations
  • 2.3 Nonhomogeneous Equations
  • References
  • 3 Integral Equations of Second Kind with Continuous and Square Integrable Kernel
  • 3.1 Fredholm Integral Equations of Second Kind with Continuous Kernel
  • 3.2 Volterra Integral Equations of Second Kind with Continuous Kernel
  • 3.3 Illustrative Examples
  • 3.4 Iterated Kernels
  • 3.5 Fredholm Theory for Integral Equation with Continuous Kernel
  • 3.6 Fredholm Integral Equations of Second Kind with Square Integrable Kernel
  • 3.6.1 Some Important Properties of Square Integrable Functions
  • 3.6.2 Method of Solution of Integral Equation with Square Integrable Kernel
  • 3.7 Fredholm Theory for Integral Equation with Square Integrable Kernel
  • References
  • 4 Integral Equations of the Second Kind with a Symmetric Kernel
  • 4.1 Symmetric Kernel
  • 4.2 Properties of Integral Equations with a Symmetric Kernel
  • 4.3 Hilbert-Schmidt Theorem
  • References
  • 5 Abel Integral Equations
  • 5.1 Solution Based on Elementary Integration
  • 5.2 Solution Based on Laplace Transform
  • References
  • Part II Integral Transform
  • 6 Fourier Transform
  • 6.1 Integral Transform: An Introduction
  • 6.2 Fourier Integral Theorem
  • 6.3 Rigorous Justification of Fourier Integral Theorem
  • 6.4 Fourier Cosine and Sine Transforms
  • 6.5 Fourier Transforms of Some Simple Functions
  • 6.6 Properties of Fourier Transform
  • 6.7 Convolution Theorem and Parseval Relation
  • 6.8 Fourier Transforms in Two or More Dimensions
  • 6.9 Application of Fourier Transforms in Solving Linear Ordinary ...
  • 6.10 Application of Fourier Sine and Cosine Transforms in Solving ...
  • 6.11 Application to Partial Differential Equations
  • 6.12 Application of Fourier Sine and Cosine Transform to the Solution ...
  • References
  • 7 Laplace Transform
  • 7.1 Derivation of Laplace Transform from Fourier Integral Theorem
  • 7.2 Laplace Inversion
  • 7.3 Operational Properties of Laplace Transform
  • 7.4 Laplace Convolution Integral
  • 7.5 Tauberian Theorems
  • 7.6 Method of Evaluation of Inverse Laplace Transform
  • 7.7 Application of Laplace Transform in Solving Ordinary Differential Equations
  • 7.8 Application Laplace Transform in Solving Partial Differential Equations
  • References
  • 8 Mellin Transform
  • 8.1 Introduction
  • 8.2 Formal Derivation of Mellin Transform
  • 8.3 Theorem on Inversion of Mellin Transform

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