A First Course in Integral Equations

The following sections are included:

• Dedication
• Contents
• Preface to the Second Edition
• Preface to the First Edition

The following sections are included:

• Definitions
• Classification of Linear Integral Equations
  • Fredholm Linear Integral Equations
  • Volterra Linear Integral Equations
  • Integro-Differential Equations
  • Singular Integral Equations
  • Volterra-Fredholm Integral Equations
  • Volterra-Fredholm Integro-Differential Equations
• Solution of an Integral Equation
• Converting Volterra Equation to an ODE
  • Differentiating Any Integral: Leibniz Rule
• Converting IVP to Volterra Equation
• Converting BVP to Fredholm Equation
• Taylor Series
• Infinite Geometric Series

The following sections are included:

• Introduction
• The Adomian Decomposition Method
  • The Modified Decomposition Method
  • The Noise Terms Phenomenon
• The Variational Iteration Method
• The Direct Computation Method
• The Successive Approximations Method
• The Method of Successive Substitutions
• Comparison between Alternative Methods
• Homogeneous Fredholm Integral Equations
• Fredholm Integral Equations of the First Kind
  • The Method of Regularization

The following sections are included:

• Introduction
• The Adomian Decomposition Method
  • The Modified Decomposition Method
  • The Noise Terms Phenomenon
• The Variational Iteration Method
• The Series Solution Method
• Converting Volterra Equation to IVP
• Successive Approximations Method
• The Method of Successive Substitutions
• Comparison between Alternative Methods
• Volterra Integral Equations of the First Kind
  • The Series Solution Method
  • Conversion of First Kind to Second Kind

The following sections are included:

• Introduction
• Fredholm Integro-Differential Equations
• The Direct Computation Method
• The Adomian Decomposition Method
  • The Modified Decomposition Method
  • The Noise Terms Phenomenon
• The Variational Iteration Method
• Converting to Fredholm Integral Equations

The following sections are included:

• Introduction
• Volterra Integro-Differential Equations
• The Series Solution Method
• The Adomian Decomposition Method
• The Variational Iteration Method
• Converting to Volterra Integral Equation
• Converting to Initial Value Problems
• Volterra Integro-Differential Equations of the First Kind

The following sections are included:

• Introduction
• Abel's Problem
• The Generalized Abel's Integral Equation
• The Weakly-Singular Volterra Integral Equations
  • The Adomian Decomposition Method
• The Weakly-Singular Fredholm Integral Equations
  • The Modified Decomposition Method

The following sections are included:

• Introduction
• Nonlinear Fredholm Integral Equations of the Second Kind
  • The Direct Computation Method
  • The Adomian Decomposition Method
  • The Variational Iteration Method
• Nonlinear Fredholm Integral Equations of the First Kind
  • The Method of Regularization
• Nonlinear Weakly-Singular Fredholm Integral Equations
  • The Modified Decomposition Method

The following sections are included:

• Introduction
• Nonlinear Volterra Integral Equations of the Second Kind
  • The Series Solution Method
  • The Adomian Decomposition Method
  • The Variational Iteration Method
• Nonlinear Volterra Integral Equations of the First Kind
  • The Series Solution Method
  • Conversion to a Volterra Equation of the Second Kind
• Nonlinear Weakly-Singular Volterra Integral Equations
  • The Modified Decomposition Method

The following sections are included:

• Introduction
• Volterra Integral Form of the Lane-Emden Equation
  • Lane-Emden Equation of the First Kind
  • Lane-Emden Equation of the Second Kind
• The Schlömilch's Integral Equation
  • The Linear Schlömilch's Integral Equation
  • The Method of Regularization
  • The Nonlinear Schlömilch's Integral Equation
• Bratu-Type Problems
  • First Bratu-Type Problem
  • Second Bratu-Type Problem
  • Third Bratu-Type Problem
• Systems of Integral Equations
  • Systems of Fredholm Integral Equations
  • Systems of Volterra Integral Equations
• Numerical Treatment of Fredholm Integral Equations
• Numerical Treatment of Volterra Integral Equations

The following sections are included:

• Appendix A: Table of Indefinite Integrals
• Appendix B: Integrals Involving Irrational Algebraic Functions
• Appendix C: Series
• Appendix D: The Error and the Gamma Functions
• Answers to Exercises

The following sections are included:

• Bibliography
• Index