A First Course in Integral Equations

The following sections are included:

• Dedication
• Contents
• Preface

The following sections are included:

• Classification of Linear Integral Equations
• Solution of an Integral Equation
• Converting Volterra Equation to an ODE
• Converting IVP to Volterra Equation
• Converting BVP to Fredholm Equation
• Taylor Series

The following sections are included:

• Adomian Decomposition Method
• The Variational Iteration Method
• The Direct Computation Method
• Successive Approximations Method
• Successive Substitutions Method
• Homogeneous Fredholm Equation
• Fredholm Integral Equation of the First Kind

The following sections are included:

• Adomian Decomposition Method
• The Variational Iteration Method
• The Series Solution Method
• Converting Volterra Equation to IVP
• Successive Approximations Method
• Successive Substitutions Method
• Volterra Equations of the First Kind

The following sections are included:

• The Direct Computation Method
• The Adomian Decomposition Method
• The Variational Iteration Method
• Converting to Fredholm Integral Equations

The following sections are included:

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

The following sections are included:

• Abel's Problem
• Generalized Abel's Problem
• The Weakly Singular Volterra Equations
• The Weakly Singular Fredholm Equations

The following sections are included:

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

The following sections are included:

• Nonlinear Volterra Integral Equations
  • 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 Equation