佤斯瓦茨所著的《线性与非线性积分方程方法及应用》共分两部分，第一部分主要对第一类、第二类线性积分方程进行了系统、深入的分析并提供各种解法；第二部分主要讲述非线性积分方程求解及其应用，针对不适定Fredholm问题、分歧点和奇异点等问题进行了系统的分析，并提供易于理解的处理方法。本书通过大量的例子讲述线性与非线性积分方程最新发展起来的高效解法，无须要求读者对抽象理论本身有很深的理解，同时也讨论了某些经典方法一些有价值的改进。

佤斯瓦茨所著的《线性与非线性积分方程方法及应用》是一本同时介绍线性和非线性积分方程的教材，分成两部分，各部分自成体系。第一部分主要对第一类、第二类线性积分方程进行了系统、深入的分析并提供各种解法；第二部分主要讲述非线性积分方程求解及其应用，针对不适定Fredholm问题、分歧点和奇异点等问题进行了系统的分析，并提供易于理解的处理方法。

《线性与非线性积分方程方法及应用》通过大量的例子讲述线性与非线性积分方程最新发展起来的高效解法，无须要求读者对抽象理论本身有很深的理解，同时也讨论了某些经典方法一些有价值的改进。书中对这些方法都给出了很好的解释，并通过对这些方法进行对比，使得读者能够快速地掌握并选择可行且高效的方法。《线性与非线性积分方程：方法及应用》提供了大量的习题，并在书后附有答案。

《线性与非线性积分方程方法及应用》可作为应用数学、工程学及其相关专业的高年级本科生和研究生教材，也可供相关领域的工程师参考。

Part I Linear Integral Equations

 1 Preliminaries

 1.1 Taylor Series

 1.2 Ordinary Differential Equations

1.2.1 First Order Linear Differential Equations

1.2.2 Second Order Linear Differential Equations

1.2.3 The Series Solution Method

 1.3 Leibnitz Rule for Differentiation of Integrals

 1.4 Reducing Multiple Integrals to Single Integrals

 1.5 Laplace Transform

1.5.1 Properties of Laplace Transforms

 1.6 Infinite Geometric Series

 References

 2 Introductory Concepts of Integral Equations

 2.1 Classification of Integral Equations

2.1.1 Fredholm Integral Equations

2.1.2 Volterra Integral Equations

2.1.3 Volterra-Fredholm Integral Equations

2.1.4 Singular Integral Equations

 2.2 Classification of Integro-Differential Equations

2.2.1 Fredholm Integro-Differential Equations

2.2.2 Volterra Integro-Differential Equations

2.2.3 Volterra-Fredholm Integro-Differential Equations

 2.3 Linearity and Homogeneity

2.3.1 Linearity Concept

2.3.2 Homogeneity Concept

 2.4 Origins of Integral Equations

 2.5 Converting IVP to Volterra Integral Equation

2.5.1 Converting Volterra Integral Equation to IVP

 2.6 Converting BVP to Fredholm Integral Equation

2.6.1 Converting Fredholm Integral Equation to BVP

 2.7 Solution of an Integral Equation

 References

 3 Volterra Integral Equations

 3.1 Introduction

 3.2 Volterra Integral Equations of the Second Kind

3.2.1 The Adomian Decomposition Method

3.2.2 The Modified Decomposition Method

3.2.3 The Noise Terms Phenomenon

3.2.4 The Variational Iteration Method

3.2.5 The Successive Approximations Method

3.2.6 The Laplace Transform Method

3.2.7 The Series Solution Method

 3.3 Volterra Integral Equations of the First Kind

3.3.1 The Series Solution Method

3.3.2 The Laplace Transform Method

3.3.3 Conversion to a Volterra Equation of the Second Kind

 References

 4  Fredholm Integral Equations

 4.1 Introduction

 4.2 Fredholm Integral Equations of the Second Kind

4.2.1 The Adomian Decomposition Method

4.2.2 The Modified Decomposition Method

4.2.3 The Noise Terms Phenomenon

4.2.4 The Variational Iteration Method

4.2.5 The Direct Computation Method

4.2.6 The Successive Approximations Method

4.2.7 The Series Solution Method

 4.3 Homogeneous Fredholm Integral Equation

4.3.1 The Direct Computation Method

 4.4 Fredholm Integral Equations of the First Kind

4.4.1 The Method of Regularization

4.4.2 The Homotopy Perturbation Method

 References

 5 Volterra Integro-Differential Equations

 5.1 Introduction

 5.2 Volterra Integro-Differential Equations of the Second Kind

5.2.1 The Adomian Decomposition Method

5.2.2 The Variational Iteration Method

 ……

Part II Nonlinear Integral Equations

Appendix