线性与非线性积分方程：方法及应用（英文版）
定价：￥110.00
作者： Abdul-Majid Wazwaz
出版社：高等教育出版社
- 高等教育出版社
- 9787040316940
- 1版
- 47265998-6
- 16开
- 790
- 理学
- 数学类
- 应用数学、物理、工程
- 研究生及以上
内容简介
本书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。
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。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。本书提供了大量 的习题，并在书后附有答案。
本书可作为应用数学、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。
目录
目录
front matter
Part I hspace betweenumberspace 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
5.2.3 The Laplace Transform Method
5.2.4 The Series Solution Method
5.2.5 Converting Volterra Integro-Differential Equations to Initial Value Problems
5.2.6 Convertingtmspace +thinmuskip .1667em Volterratmspace +thickmuskip .2777em Integro-Differentialtmspace +thickmuskip .2777em Equation to Volterra Integral Equation
5.3 Volterra Integro-Differential Equations of the First Kind
5.3.1 Laplace Transform Method
5.3.2 The Variational Iteration Method
References
6 Fredholm Integro-Differential Equations
6.1 Introduction
6.2 Fredholm Integro-Differential Equations of the Second Kind
6.2.1 The Direct Computation Method
6.2.2 The Variational Iteration Method
6.2.3 The Adomian Decomposition Method
6.2.4 The Series Solution Method
References
7 Abel's Integral Equation and Singular Integral Equations
7.1 Introduction
7.2 Abel's Integral Equation
7.2.1 The Laplace Transform Method
7.3 The Generalized Abel's Integral Equation
7.3.1 The Laplace Transform Method
7.3.2 The Main Generalized Abel Equation
7.4 The Weakly Singular Volterra Equations
7.4.1 The Adomian Decomposition Method
7.4.2 The Successive Approximations Method
7.4.3 The Laplace Transform Method
References
8 Volterra-Fredholm Integral Equations
8.1 Introduction
8.2 The Volterra-Fredholm Integral Equations
8.2.1 The Series Solution Method
8.2.2 The Adomian Decomposition Method
8.3 The Mixed Volterra-Fredholm Integral Equations
8.3.1 The Series Solution Method
8.3.2 The Adomian Decomposition Method
8.4 The Mixed Volterra-Fredholm Integral Equations in Two Variables
8.4.1 The Modified Decomposition Method
References
9 Volterra-Fredholm Integro-Differential Equations
9.1 Introduction
9.2 The Volterra-Fredholm Integro-Differential Equation
9.2.1 The Series Solution Method
9.2.2 The Variational Iteration Method
9.3 The Mixed Volterra-Fredholm Integro-Differential Equations
9.3.1 The Direct Computation Method
9.3.2 The Series Solution Method
9.4 The Mixed Volterra-Fredholm Integro-Differential Equations in Two Variables
9.4.1 The Modified Decomposition Method
References
10 Systems of Volterra Integral Equations
10.1 Introduction
10.2 Systems of Volterra Integral Equations of the hspace*1.7mm Second Kind
10.2.1 The Adomian Decomposition Method
10.2.2 The Laplace Transform Method
10.3 Systems of Volterra Integral Equations of the First Kind
10.3.1 The Laplace Transform Method
10.3.2 Conversion to a Volterra System of the hspace*2.5mm Second Kind
10.4 Systems of Volterra Integro-Differential Equations
10.4.1 The Variational Iteration Method
10.4.2 The Laplace Transform Method
References
11 Systems of Fredholm Integral Equations
11.1 Introduction
11.2 Systems of Fredholm Integral Equations
11.2.1 The Adomian Decomposition Method
11.2.2 The Direct Computation Method
11.3 Systems of Fredholm Integro-Differential Equations
11.3.1 The Direct Computation Method
11.3.2 The Variational Iteration Method
References
12 Systems of Singular Integral Equations
12.1 Introduction
12.2 Systems of Generalized Abel Integral Equations
12.2.1 Systems of Generalized Abel Integral Equations in hspace*2.5mm Two Unknowns
12.2.2 Systems of Generalized Abel Integral Equations in hspace*2.5mm Three Unknowns
12.3 Systems of the Weakly Singular Volterra Integral hspace*1.7mm Equations
12.3.1 The Laplace Transform Method
12.3.2 The Adomian Decomposition Method
References
Part IIhspace betweenumberspace Nonlinear Integral Equations
13 Nonlinear Volterra Integral Equations
13.1 Introduction
13.2 Existence of the Solution for Nonlinear Volterra Integral hspace*1.7mm Equations
13.3 Nonlinear Volterra Integral Equations of the Second Kind
13.3.1 The Successive Approximations Method
13.3.2 The Series Solution Method
13.3.3 The Adomian Decomposition Method
13.4 Nonlinear Volterra Integral Equations of the First Kind
13.4.1 The Laplace Transform Method
13.4.2 Conversion to a Volterra Equation of the hspace*2.5mm Second Kind
13.5 Systems of Nonlinear Volterra Integral Equations
13.5.1 Systems of Nonlinear Volterra Integral Equations of hspace*2.5mm the Second Kind
13.5.2 Systems of Nonlinear Volterra Integral Equations of hspace*2.5mm the First Kind
References
14 Nonlinear Volterra Integro-Differential Equations
14.1 Introduction
14.2 Nonlinear Volterra Integro-Differential Equations of the hspace*1.7mm Second Kind
14.2.1 The Combined Laplace Transform-Adomian hspace*2.5mm Decomposition Method
14.2.2 The Variational Iteration Method
14.2.3 The Series Solution Method
14.3 Nonlinear Volterra Integro-Differential Equations of the hspace*1.7mm First Kind
14.3.1 The Combined Laplace Transform-Adomian hspace*2.5mm Decomposition Method
14.3.2 Conversion to Nonlinear Volterra Equation of the hspace*2.5mm Second Kind
14.4 Systems of Nonlinear Volterra Integro-Differential hspace*1.7mm Equations
14.4.1 The Variational Iteration Method
14.4.2 The Combined Laplace Transform-Adomian hspace*2.5mm Decomposition Method
References
15 Nonlinear Fredholm Integral Equations
15.1 Introduction
15.2 Existence of the Solution for Nonlinear Fredholm Integral hspace*1.7mm Equations
15.2.1 Bifurcation Points and Singular Points
15.3 Nonlinear Fredholm Integral Equations of the hspace*1.7mm Second Kind
15.3.1 The Direct Computation Method
15.3.2 The Series Solution Method
15.3.3 The Adomian Decomposition Method
15.3.4 The Successive Approximations Method
15.4 Homogeneous Nonlinear Fredholm Integral Equations
15.4.1 The Direct Computation Method
15.5 Nonlinear Fredholm Integral Equations of the First Kind
15.5.1 The Method of Regularization
15.5.2 The Homotopy Perturbation Method
15.6 Systems of Nonlinear Fredholm Integral Equations
15.6.1 The Direct Computation Method
15.6.2 The Modified Adomian Decomposition Method
References
16 Nonlinear Fredholm Integro-Differential Equations
16.1 Introduction
16.2 Nonlinear Fredholm Integro-Differential Equations
16.2.1 The Direct Computation Method
16.2.2 The Variational Iteration Method
16.2.3 The Series Solution Method
16.3 Homogeneous Nonlinear Fredholm Integro-Differential hspace*1.7mm Equations
16.3.1 The Direct Computation Method
16.4 Systems of Nonlinear Fredholm Integro-Differential hspace*1.7mm Equations
16.4.1 The Direct Computation Method
16.4.2 The Variational Iteration Method
References
17 Nonlinear Singular Integral Equations
17.1 Introduction
17.2 Nonlinear Abel's Integral Equation
17.2.1 The Laplace Transform Method
17.3 The Generalized Nonlinear Abel Equation
17.3.1 The Laplace Transform Method
17.3.2 The Main Generalized Nonlinear Abel Equation
17.4 The Nonlinear Weakly-Singular Volterra Equations
17.4.1 The Adomian Decomposition Method
17.5 Systems of Nonlinear Weakly-Singular Volterra Integral hspace*1.7mm Equations
17.5.1 The Modified Adomian Decomposition Method
References
18 Applications of Integral Equations
18.1 Introduction
18.2 Volterra's Population Model
18.2.1 The Variational Iteration Method
18.2.2 The Series Solution Method
18.2.3 The Pad'e Approximants
18.3 Integral Equations with Logarithmic Kernels
18.3.1 Second Kind Fredholm Integral Equation with a hspace*2.5mm Logarithmic Kernel
18.3.2 First Kind Fredholm Integral Equation with a hspace*2.5mm Logarithmic Kernel
18.3.3 Another First Kind Fredholm Integral Equation hspace*2.5mm with a Logarithmic Kernel
18.4 The Fresnel Integrals
18.5 The Thomas-Fermi Equation
18.6 Heat Transfer and Heat Radiation
18.6.1 Heat Transfer: Lighthill Singular Integral Equation
18.6.2 Heat Radiation in a Semi-Infinite Solid
References
Appendix A hspace*18mm Table of Indefinite Integrals
A.1 Basic Forms
A.2 Trigonometric Forms
A.3 Inverse Trigonometric Forms
A.4 Exponential and Logarithmic Forms
A.5 Hyperbolic Forms
A.6 Other Forms
Appendix B hspace*18mm Integrals Involving Irrational Algebraic hspace*18mm Functions
B.1 Integrals Involving $frac t^n sqrt x-t $, $n$ is an integer, $n geqslant 0$
B.2 Integrals Involving $frac t^frac n 2 sqrt x-t $, $n$ is an odd integer, $n geqslant 1$
Appendix C hspace*18mm Series Representations
C.1 Exponential Functions Series
C.2 Trigonometric Functions
C.3 Inverse Trigonometric Functions
C.4 Hyperbolic Functions
C.5 Inverse Hyperbolic Functions
C.6 Logarithmic Functions
Appendix D hspace*18mm The Error and the Complementary Error Functions
D.1 The Error Function
D.2 The Complementary Error Function
Appendix E hspace*18mm Gamma Function
Appendix F hspace*18mm Infinite Series
F.1 Numerical Series
F.2 Trigonometric Series
Appendix G hspace*18mm The Fresnel Integrals
G.1 The Fresnel Cosine Integral
G.2 The Fresnel Sine Integral
Answers
Index
版权
front matter
Part I hspace betweenumberspace 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
5.2.3 The Laplace Transform Method
5.2.4 The Series Solution Method
5.2.5 Converting Volterra Integro-Differential Equations to Initial Value Problems
5.2.6 Convertingtmspace +thinmuskip .1667em Volterratmspace +thickmuskip .2777em Integro-Differentialtmspace +thickmuskip .2777em Equation to Volterra Integral Equation
5.3 Volterra Integro-Differential Equations of the First Kind
5.3.1 Laplace Transform Method
5.3.2 The Variational Iteration Method
References
6 Fredholm Integro-Differential Equations
6.1 Introduction
6.2 Fredholm Integro-Differential Equations of the Second Kind
6.2.1 The Direct Computation Method
6.2.2 The Variational Iteration Method
6.2.3 The Adomian Decomposition Method
6.2.4 The Series Solution Method
References
7 Abel's Integral Equation and Singular Integral Equations
7.1 Introduction
7.2 Abel's Integral Equation
7.2.1 The Laplace Transform Method
7.3 The Generalized Abel's Integral Equation
7.3.1 The Laplace Transform Method
7.3.2 The Main Generalized Abel Equation
7.4 The Weakly Singular Volterra Equations
7.4.1 The Adomian Decomposition Method
7.4.2 The Successive Approximations Method
7.4.3 The Laplace Transform Method
References
8 Volterra-Fredholm Integral Equations
8.1 Introduction
8.2 The Volterra-Fredholm Integral Equations
8.2.1 The Series Solution Method
8.2.2 The Adomian Decomposition Method
8.3 The Mixed Volterra-Fredholm Integral Equations
8.3.1 The Series Solution Method
8.3.2 The Adomian Decomposition Method
8.4 The Mixed Volterra-Fredholm Integral Equations in Two Variables
8.4.1 The Modified Decomposition Method
References
9 Volterra-Fredholm Integro-Differential Equations
9.1 Introduction
9.2 The Volterra-Fredholm Integro-Differential Equation
9.2.1 The Series Solution Method
9.2.2 The Variational Iteration Method
9.3 The Mixed Volterra-Fredholm Integro-Differential Equations
9.3.1 The Direct Computation Method
9.3.2 The Series Solution Method
9.4 The Mixed Volterra-Fredholm Integro-Differential Equations in Two Variables
9.4.1 The Modified Decomposition Method
References
10 Systems of Volterra Integral Equations
10.1 Introduction
10.2 Systems of Volterra Integral Equations of the hspace*1.7mm Second Kind
10.2.1 The Adomian Decomposition Method
10.2.2 The Laplace Transform Method
10.3 Systems of Volterra Integral Equations of the First Kind
10.3.1 The Laplace Transform Method
10.3.2 Conversion to a Volterra System of the hspace*2.5mm Second Kind
10.4 Systems of Volterra Integro-Differential Equations
10.4.1 The Variational Iteration Method
10.4.2 The Laplace Transform Method
References
11 Systems of Fredholm Integral Equations
11.1 Introduction
11.2 Systems of Fredholm Integral Equations
11.2.1 The Adomian Decomposition Method
11.2.2 The Direct Computation Method
11.3 Systems of Fredholm Integro-Differential Equations
11.3.1 The Direct Computation Method
11.3.2 The Variational Iteration Method
References
12 Systems of Singular Integral Equations
12.1 Introduction
12.2 Systems of Generalized Abel Integral Equations
12.2.1 Systems of Generalized Abel Integral Equations in hspace*2.5mm Two Unknowns
12.2.2 Systems of Generalized Abel Integral Equations in hspace*2.5mm Three Unknowns
12.3 Systems of the Weakly Singular Volterra Integral hspace*1.7mm Equations
12.3.1 The Laplace Transform Method
12.3.2 The Adomian Decomposition Method
References
Part IIhspace betweenumberspace Nonlinear Integral Equations
13 Nonlinear Volterra Integral Equations
13.1 Introduction
13.2 Existence of the Solution for Nonlinear Volterra Integral hspace*1.7mm Equations
13.3 Nonlinear Volterra Integral Equations of the Second Kind
13.3.1 The Successive Approximations Method
13.3.2 The Series Solution Method
13.3.3 The Adomian Decomposition Method
13.4 Nonlinear Volterra Integral Equations of the First Kind
13.4.1 The Laplace Transform Method
13.4.2 Conversion to a Volterra Equation of the hspace*2.5mm Second Kind
13.5 Systems of Nonlinear Volterra Integral Equations
13.5.1 Systems of Nonlinear Volterra Integral Equations of hspace*2.5mm the Second Kind
13.5.2 Systems of Nonlinear Volterra Integral Equations of hspace*2.5mm the First Kind
References
14 Nonlinear Volterra Integro-Differential Equations
14.1 Introduction
14.2 Nonlinear Volterra Integro-Differential Equations of the hspace*1.7mm Second Kind
14.2.1 The Combined Laplace Transform-Adomian hspace*2.5mm Decomposition Method
14.2.2 The Variational Iteration Method
14.2.3 The Series Solution Method
14.3 Nonlinear Volterra Integro-Differential Equations of the hspace*1.7mm First Kind
14.3.1 The Combined Laplace Transform-Adomian hspace*2.5mm Decomposition Method
14.3.2 Conversion to Nonlinear Volterra Equation of the hspace*2.5mm Second Kind
14.4 Systems of Nonlinear Volterra Integro-Differential hspace*1.7mm Equations
14.4.1 The Variational Iteration Method
14.4.2 The Combined Laplace Transform-Adomian hspace*2.5mm Decomposition Method
References
15 Nonlinear Fredholm Integral Equations
15.1 Introduction
15.2 Existence of the Solution for Nonlinear Fredholm Integral hspace*1.7mm Equations
15.2.1 Bifurcation Points and Singular Points
15.3 Nonlinear Fredholm Integral Equations of the hspace*1.7mm Second Kind
15.3.1 The Direct Computation Method
15.3.2 The Series Solution Method
15.3.3 The Adomian Decomposition Method
15.3.4 The Successive Approximations Method
15.4 Homogeneous Nonlinear Fredholm Integral Equations
15.4.1 The Direct Computation Method
15.5 Nonlinear Fredholm Integral Equations of the First Kind
15.5.1 The Method of Regularization
15.5.2 The Homotopy Perturbation Method
15.6 Systems of Nonlinear Fredholm Integral Equations
15.6.1 The Direct Computation Method
15.6.2 The Modified Adomian Decomposition Method
References
16 Nonlinear Fredholm Integro-Differential Equations
16.1 Introduction
16.2 Nonlinear Fredholm Integro-Differential Equations
16.2.1 The Direct Computation Method
16.2.2 The Variational Iteration Method
16.2.3 The Series Solution Method
16.3 Homogeneous Nonlinear Fredholm Integro-Differential hspace*1.7mm Equations
16.3.1 The Direct Computation Method
16.4 Systems of Nonlinear Fredholm Integro-Differential hspace*1.7mm Equations
16.4.1 The Direct Computation Method
16.4.2 The Variational Iteration Method
References
17 Nonlinear Singular Integral Equations
17.1 Introduction
17.2 Nonlinear Abel's Integral Equation
17.2.1 The Laplace Transform Method
17.3 The Generalized Nonlinear Abel Equation
17.3.1 The Laplace Transform Method
17.3.2 The Main Generalized Nonlinear Abel Equation
17.4 The Nonlinear Weakly-Singular Volterra Equations
17.4.1 The Adomian Decomposition Method
17.5 Systems of Nonlinear Weakly-Singular Volterra Integral hspace*1.7mm Equations
17.5.1 The Modified Adomian Decomposition Method
References
18 Applications of Integral Equations
18.1 Introduction
18.2 Volterra's Population Model
18.2.1 The Variational Iteration Method
18.2.2 The Series Solution Method
18.2.3 The Pad'e Approximants
18.3 Integral Equations with Logarithmic Kernels
18.3.1 Second Kind Fredholm Integral Equation with a hspace*2.5mm Logarithmic Kernel
18.3.2 First Kind Fredholm Integral Equation with a hspace*2.5mm Logarithmic Kernel
18.3.3 Another First Kind Fredholm Integral Equation hspace*2.5mm with a Logarithmic Kernel
18.4 The Fresnel Integrals
18.5 The Thomas-Fermi Equation
18.6 Heat Transfer and Heat Radiation
18.6.1 Heat Transfer: Lighthill Singular Integral Equation
18.6.2 Heat Radiation in a Semi-Infinite Solid
References
Appendix A hspace*18mm Table of Indefinite Integrals
A.1 Basic Forms
A.2 Trigonometric Forms
A.3 Inverse Trigonometric Forms
A.4 Exponential and Logarithmic Forms
A.5 Hyperbolic Forms
A.6 Other Forms
Appendix B hspace*18mm Integrals Involving Irrational Algebraic hspace*18mm Functions
B.1 Integrals Involving $frac t^n sqrt x-t $, $n$ is an integer, $n geqslant 0$
B.2 Integrals Involving $frac t^frac n 2 sqrt x-t $, $n$ is an odd integer, $n geqslant 1$
Appendix C hspace*18mm Series Representations
C.1 Exponential Functions Series
C.2 Trigonometric Functions
C.3 Inverse Trigonometric Functions
C.4 Hyperbolic Functions
C.5 Inverse Hyperbolic Functions
C.6 Logarithmic Functions
Appendix D hspace*18mm The Error and the Complementary Error Functions
D.1 The Error Function
D.2 The Complementary Error Function
Appendix E hspace*18mm Gamma Function
Appendix F hspace*18mm Infinite Series
F.1 Numerical Series
F.2 Trigonometric Series
Appendix G hspace*18mm The Fresnel Integrals
G.1 The Fresnel Cosine Integral
G.2 The Fresnel Sine Integral
Answers
Index
版权
front matter
Part I hspace betweenumberspace 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
5.2.3 The Laplace Transform Method
5.2.4 The Series Solution Method
5.2.5 Converting Volterra Integro-Differential Equations to Initial Value Problems
5.2.6 Convertingtmspace +thinmuskip .1667em Volterratmspace +thickmuskip .2777em Integro-Differentialtmspace +thickmuskip .2777em Equation to Volterra Integral Equation
5.3 Volterra Integro-Differential Equations of the First Kind
5.3.1 Laplace Transform Method
5.3.2 The Variational Iteration Method
References
6 Fredholm Integro-Differential Equations
6.1 Introduction
6.2 Fredholm Integro-Differential Equations of the Second Kind
6.2.1 The Direct Computation Method
6.2.2 The Variational Iteration Method
6.2.3 The Adomian Decomposition Method
6.2.4 The Series Solution Method
References
7 Abel's Integral Equation and Singular Integral Equations
7.1 Introduction
7.2 Abel's Integral Equation
7.2.1 The Laplace Transform Method
7.3 The Generalized Abel's Integral Equation
7.3.1 The Laplace Transform Method
7.3.2 The Main Generalized Abel Equation
7.4 The Weakly Singular Volterra Equations
7.4.1 The Adomian Decomposition Method
7.4.2 The Successive Approximations Method
7.4.3 The Laplace Transform Method
References
8 Volterra-Fredholm Integral Equations
8.1 Introduction
8.2 The Volterra-Fredholm Integral Equations
8.2.1 The Series Solution Method
8.2.2 The Adomian Decomposition Method
8.3 The Mixed Volterra-Fredholm Integral Equations
8.3.1 The Series Solution Method
8.3.2 The Adomian Decomposition Method
8.4 The Mixed Volterra-Fredholm Integral Equations in Two Variables
8.4.1 The Modified Decomposition Method
References
9 Volterra-Fredholm Integro-Differential Equations
9.1 Introduction
9.2 The Volterra-Fredholm Integro-Differential Equation
9.2.1 The Series Solution Method
9.2.2 The Variational Iteration Method
9.3 The Mixed Volterra-Fredholm Integro-Differential Equations
9.3.1 The Direct Computation Method
9.3.2 The Series Solution Method
9.4 The Mixed Volterra-Fredholm Integro-Differential Equations in Two Variables
9.4.1 The Modified Decomposition Method
References
10 Systems of Volterra Integral Equations
10.1 Introduction
10.2 Systems of Volterra Integral Equations of the hspace*1.7mm Second Kind
10.2.1 The Adomian Decomposition Method
10.2.2 The Laplace Transform Method
10.3 Systems of Volterra Integral Equations of the First Kind
10.3.1 The Laplace Transform Method
10.3.2 Conversion to a Volterra System of the hspace*2.5mm Second Kind
10.4 Systems of Volterra Integro-Differential Equations
10.4.1 The Variational Iteration Method
10.4.2 The Laplace Transform Method
References
11 Systems of Fredholm Integral Equations
11.1 Introduction
11.2 Systems of Fredholm Integral Equations
11.2.1 The Adomian Decomposition Method
11.2.2 The Direct Computation Method
11.3 Systems of Fredholm Integro-Differential Equations
11.3.1 The Direct Computation Method
11.3.2 The Variational Iteration Method
References
12 Systems of Singular Integral Equations
12.1 Introduction
12.2 Systems of Generalized Abel Integral Equations
12.2.1 Systems of Generalized Abel Integral Equations in hspace*2.5mm Two Unknowns
12.2.2 Systems of Generalized Abel Integral Equations in hspace*2.5mm Three Unknowns
12.3 Systems of the Weakly Singular Volterra Integral hspace*1.7mm Equations
12.3.1 The Laplace Transform Method
12.3.2 The Adomian Decomposition Method
References
Part IIhspace betweenumberspace Nonlinear Integral Equations
13 Nonlinear Volterra Integral Equations
13.1 Introduction
13.2 Existence of the Solution for Nonlinear Volterra Integral hspace*1.7mm Equations
13.3 Nonlinear Volterra Integral Equations of the Second Kind
13.3.1 The Successive Approximations Method
13.3.2 The Series Solution Method
13.3.3 The Adomian Decomposition Method
13.4 Nonlinear Volterra Integral Equations of the First Kind
13.4.1 The Laplace Transform Method
13.4.2 Conversion to a Volterra Equation of the hspace*2.5mm Second Kind
13.5 Systems of Nonlinear Volterra Integral Equations
13.5.1 Systems of Nonlinear Volterra Integral Equations of hspace*2.5mm the Second Kind
13.5.2 Systems of Nonlinear Volterra Integral Equations of hspace*2.5mm the First Kind
References
14 Nonlinear Volterra Integro-Differential Equations
14.1 Introduction
14.2 Nonlinear Volterra Integro-Differential Equations of the hspace*1.7mm Second Kind
14.2.1 The Combined Laplace Transform-Adomian hspace*2.5mm Decomposition Method
14.2.2 The Variational Iteration Method
14.2.3 The Series Solution Method
14.3 Nonlinear Volterra Integro-Differential Equations of the hspace*1.7mm First Kind
14.3.1 The Combined Laplace Transform-Adomian hspace*2.5mm Decomposition Method
14.3.2 Conversion to Nonlinear Volterra Equation of the hspace*2.5mm Second Kind
14.4 Systems of Nonlinear Volterra Integro-Differential hspace*1.7mm Equations
14.4.1 The Variational Iteration Method
14.4.2 The Combined Laplace Transform-Adomian hspace*2.5mm Decomposition Method
References
15 Nonlinear Fredholm Integral Equations
15.1 Introduction
15.2 Existence of the Solution for Nonlinear Fredholm Integral hspace*1.7mm Equations
15.2.1 Bifurcation Points and Singular Points
15.3 Nonlinear Fredholm Integral Equations of the hspace*1.7mm Second Kind
15.3.1 The Direct Computation Method
15.3.2 The Series Solution Method
15.3.3 The Adomian Decomposition Method
15.3.4 The Successive Approximations Method
15.4 Homogeneous Nonlinear Fredholm Integral Equations
15.4.1 The Direct Computation Method
15.5 Nonlinear Fredholm Integral Equations of the First Kind
15.5.1 The Method of Regularization
15.5.2 The Homotopy Perturbation Method
15.6 Systems of Nonlinear Fredholm Integral Equations
15.6.1 The Direct Computation Method
15.6.2 The Modified Adomian Decomposition Method
References
16 Nonlinear Fredholm Integro-Differential Equations
16.1 Introduction
16.2 Nonlinear Fredholm Integro-Differential Equations
16.2.1 The Direct Computation Method
16.2.2 The Variational Iteration Method
16.2.3 The Series Solution Method
16.3 Homogeneous Nonlinear Fredholm Integro-Differential hspace*1.7mm Equations
16.3.1 The Direct Computation Method
16.4 Systems of Nonlinear Fredholm Integro-Differential hspace*1.7mm Equations
16.4.1 The Direct Computation Method
16.4.2 The Variational Iteration Method
References
17 Nonlinear Singular Integral Equations
17.1 Introduction
17.2 Nonlinear Abel's Integral Equation
17.2.1 The Laplace Transform Method
17.3 The Generalized Nonlinear Abel Equation
17.3.1 The Laplace Transform Method
17.3.2 The Main Generalized Nonlinear Abel Equation
17.4 The Nonlinear Weakly-Singular Volterra Equations
17.4.1 The Adomian Decomposition Method
17.5 Systems of Nonlinear Weakly-Singular Volterra Integral hspace*1.7mm Equations
17.5.1 The Modified Adomian Decomposition Method
References
18 Applications of Integral Equations
18.1 Introduction
18.2 Volterra's Population Model
18.2.1 The Variational Iteration Method
18.2.2 The Series Solution Method
18.2.3 The Pad'e Approximants
18.3 Integral Equations with Logarithmic Kernels
18.3.1 Second Kind Fredholm Integral Equation with a hspace*2.5mm Logarithmic Kernel
18.3.2 First Kind Fredholm Integral Equation with a hspace*2.5mm Logarithmic Kernel
18.3.3 Another First Kind Fredholm Integral Equation hspace*2.5mm with a Logarithmic Kernel
18.4 The Fresnel Integrals
18.5 The Thomas-Fermi Equation
18.6 Heat Transfer and Heat Radiation
18.6.1 Heat Transfer: Lighthill Singular Integral Equation
18.6.2 Heat Radiation in a Semi-Infinite Solid
References
Appendix A hspace*18mm Table of Indefinite Integrals
A.1 Basic Forms
A.2 Trigonometric Forms
A.3 Inverse Trigonometric Forms
A.4 Exponential and Logarithmic Forms
A.5 Hyperbolic Forms
A.6 Other Forms
Appendix B hspace*18mm Integrals Involving Irrational Algebraic hspace*18mm Functions
B.1 Integrals Involving $frac t^n sqrt x-t $, $n$ is an integer, $n geqslant 0$
B.2 Integrals Involving $frac t^frac n 2 sqrt x-t $, $n$ is an odd integer, $n geqslant 1$
Appendix C hspace*18mm Series Representations
C.1 Exponential Functions Series
C.2 Trigonometric Functions
C.3 Inverse Trigonometric Functions
C.4 Hyperbolic Functions
C.5 Inverse Hyperbolic Functions
C.6 Logarithmic Functions
Appendix D hspace*18mm The Error and the Complementary Error Functions
D.1 The Error Function
D.2 The Complementary Error Function
Appendix E hspace*18mm Gamma Function
Appendix F hspace*18mm Infinite Series
F.1 Numerical Series
F.2 Trigonometric Series
Appendix G hspace*18mm The Fresnel Integrals
G.1 The Fresnel Cosine Integral
G.2 The Fresnel Sine Integral
Answers
Index
版权
front matter
Part I hspace betweenumberspace 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
5.2.3 The Laplace Transform Method
5.2.4 The Series Solution Method
5.2.5 Converting Volterra Integro-Differential Equations to Initial Value Problems
5.2.6 Convertingtmspace +thinmuskip .1667em Volterratmspace +thickmuskip .2777em Integro-Differentialtmspace +thickmuskip .2777em Equation to Volterra Integral Equation
5.3 Volterra Integro-Differential Equations of the First Kind
5.3.1 Laplace Transform Method
5.3.2 The Variational Iteration Method
References
6 Fredholm Integro-Differential Equations
6.1 Introduction
6.2 Fredholm Integro-Differential Equations of the Second Kind
6.2.1 The Direct Computation Method
6.2.2 The Variational Iteration Method
6.2.3 The Adomian Decomposition Method
6.2.4 The Series Solution Method
References
7 Abel's Integral Equation and Singular Integral Equations
7.1 Introduction
7.2 Abel's Integral Equation
7.2.1 The Laplace Transform Method
7.3 The Generalized Abel's Integral Equation
7.3.1 The Laplace Transform Method
7.3.2 The Main Generalized Abel Equation
7.4 The Weakly Singular Volterra Equations
7.4.1 The Adomian Decomposition Method
7.4.2 The Successive Approximations Method
7.4.3 The Laplace Transform Method
References
8 Volterra-Fredholm Integral Equations
8.1 Introduction
8.2 The Volterra-Fredholm Integral Equations
8.2.1 The Series Solution Method
8.2.2 The Adomian Decomposition Method
8.3 The Mixed Volterra-Fredholm Integral Equations
8.3.1 The Series Solution Method
8.3.2 The Adomian Decomposition Method
8.4 The Mixed Volterra-Fredholm Integral Equations in Two Variables
8.4.1 The Modified Decomposition Method
References
9 Volterra-Fredholm Integro-Differential Equations
9.1 Introduction
9.2 The Volterra-Fredholm Integro-Differential Equation
9.2.1 The Series Solution Method
9.2.2 The Variational Iteration Method
9.3 The Mixed Volterra-Fredholm Integro-Differential Equations
9.3.1 The Direct Computation Method
9.3.2 The Series Solution Method
9.4 The Mixed Volterra-Fredholm Integro-Differential Equations in Two Variables
9.4.1 The Modified Decomposition Method
References
10 Systems of Volterra Integral Equations
10.1 Introduction
10.2 Systems of Volterra Integral Equations of the hspace*1.7mm Second Kind
10.2.1 The Adomian Decomposition Method
10.2.2 The Laplace Transform Method
10.3 Systems of Volterra Integral Equations of the First Kind
10.3.1 The Laplace Transform Method
10.3.2 Conversion to a Volterra System of the hspace*2.5mm Second Kind
10.4 Systems of Volterra Integro-Differential Equations
10.4.1 The Variational Iteration Method
10.4.2 The Laplace Transform Method
References
11 Systems of Fredholm Integral Equations
11.1 Introduction
11.2 Systems of Fredholm Integral Equations
11.2.1 The Adomian Decomposition Method
11.2.2 The Direct Computation Method
11.3 Systems of Fredholm Integro-Differential Equations
11.3.1 The Direct Computation Method
11.3.2 The Variational Iteration Method
References
12 Systems of Singular Integral Equations
12.1 Introduction
12.2 Systems of Generalized Abel Integral Equations
12.2.1 Systems of Generalized Abel Integral Equations in hspace*2.5mm Two Unknowns
12.2.2 Systems of Generalized Abel Integral Equations in hspace*2.5mm Three Unknowns
12.3 Systems of the Weakly Singular Volterra Integral hspace*1.7mm Equations
12.3.1 The Laplace Transform Method
12.3.2 The Adomian Decomposition Method
References
Part IIhspace betweenumberspace Nonlinear Integral Equations
13 Nonlinear Volterra Integral Equations
13.1 Introduction
13.2 Existence of the Solution for Nonlinear Volterra Integral hspace*1.7mm Equations
13.3 Nonlinear Volterra Integral Equations of the Second Kind
13.3.1 The Successive Approximations Method
13.3.2 The Series Solution Method
13.3.3 The Adomian Decomposition Method
13.4 Nonlinear Volterra Integral Equations of the First Kind
13.4.1 The Laplace Transform Method
13.4.2 Conversion to a Volterra Equation of the hspace*2.5mm Second Kind
13.5 Systems of Nonlinear Volterra Integral Equations
13.5.1 Systems of Nonlinear Volterra Integral Equations of hspace*2.5mm the Second Kind
13.5.2 Systems of Nonlinear Volterra Integral Equations of hspace*2.5mm the First Kind
References
14 Nonlinear Volterra Integro-Differential Equations
14.1 Introduction
14.2 Nonlinear Volterra Integro-Differential Equations of the hspace*1.7mm Second Kind
14.2.1 The Combined Laplace Transform-Adomian hspace*2.5mm Decomposition Method
14.2.2 The Variational Iteration Method
14.2.3 The Series Solution Method
14.3 Nonlinear Volterra Integro-Differential Equations of the hspace*1.7mm First Kind
14.3.1 The Combined Laplace Transform-Adomian hspace*2.5mm Decomposition Method
14.3.2 Conversion to Nonlinear Volterra Equation of the hspace*2.5mm Second Kind
14.4 Systems of Nonlinear Volterra Integro-Differential hspace*1.7mm Equations
14.4.1 The Variational Iteration Method
14.4.2 The Combined Laplace Transform-Adomian hspace*2.5mm Decomposition Method
References
15 Nonlinear Fredholm Integral Equations
15.1 Introduction
15.2 Existence of the Solution for Nonlinear Fredholm Integral hspace*1.7mm Equations
15.2.1 Bifurcation Points and Singular Points
15.3 Nonlinear Fredholm Integral Equations of the hspace*1.7mm Second Kind
15.3.1 The Direct Computation Method
15.3.2 The Series Solution Method
15.3.3 The Adomian Decomposition Method
15.3.4 The Successive Approximations Method
15.4 Homogeneous Nonlinear Fredholm Integral Equations
15.4.1 The Direct Computation Method
15.5 Nonlinear Fredholm Integral Equations of the First Kind
15.5.1 The Method of Regularization
15.5.2 The Homotopy Perturbation Method
15.6 Systems of Nonlinear Fredholm Integral Equations
15.6.1 The Direct Computation Method
15.6.2 The Modified Adomian Decomposition Method
References
16 Nonlinear Fredholm Integro-Differential Equations
16.1 Introduction
16.2 Nonlinear Fredholm Integro-Differential Equations
16.2.1 The Direct Computation Method
16.2.2 The Variational Iteration Method
16.2.3 The Series Solution Method
16.3 Homogeneous Nonlinear Fredholm Integro-Differential hspace*1.7mm Equations
16.3.1 The Direct Computation Method
16.4 Systems of Nonlinear Fredholm Integro-Differential hspace*1.7mm Equations
16.4.1 The Direct Computation Method
16.4.2 The Variational Iteration Method
References
17 Nonlinear Singular Integral Equations
17.1 Introduction
17.2 Nonlinear Abel's Integral Equation
17.2.1 The Laplace Transform Method
17.3 The Generalized Nonlinear Abel Equation
17.3.1 The Laplace Transform Method
17.3.2 The Main Generalized Nonlinear Abel Equation
17.4 The Nonlinear Weakly-Singular Volterra Equations
17.4.1 The Adomian Decomposition Method
17.5 Systems of Nonlinear Weakly-Singular Volterra Integral hspace*1.7mm Equations
17.5.1 The Modified Adomian Decomposition Method
References
18 Applications of Integral Equations
18.1 Introduction
18.2 Volterra's Population Model
18.2.1 The Variational Iteration Method
18.2.2 The Series Solution Method
18.2.3 The Pad'e Approximants
18.3 Integral Equations with Logarithmic Kernels
18.3.1 Second Kind Fredholm Integral Equation with a hspace*2.5mm Logarithmic Kernel
18.3.2 First Kind Fredholm Integral Equation with a hspace*2.5mm Logarithmic Kernel
18.3.3 Another First Kind Fredholm Integral Equation hspace*2.5mm with a Logarithmic Kernel
18.4 The Fresnel Integrals
18.5 The Thomas-Fermi Equation
18.6 Heat Transfer and Heat Radiation
18.6.1 Heat Transfer: Lighthill Singular Integral Equation
18.6.2 Heat Radiation in a Semi-Infinite Solid
References
Appendix A hspace*18mm Table of Indefinite Integrals
A.1 Basic Forms
A.2 Trigonometric Forms
A.3 Inverse Trigonometric Forms
A.4 Exponential and Logarithmic Forms
A.5 Hyperbolic Forms
A.6 Other Forms
Appendix B hspace*18mm Integrals Involving Irrational Algebraic hspace*18mm Functions
B.1 Integrals Involving $frac t^n sqrt x-t $, $n$ is an integer, $n geqslant 0$
B.2 Integrals Involving $frac t^frac n 2 sqrt x-t $, $n$ is an odd integer, $n geqslant 1$
Appendix C hspace*18mm Series Representations
C.1 Exponential Functions Series
C.2 Trigonometric Functions
C.3 Inverse Trigonometric Functions
C.4 Hyperbolic Functions
C.5 Inverse Hyperbolic Functions
C.6 Logarithmic Functions
Appendix D hspace*18mm The Error and the Complementary Error Functions
D.1 The Error Function
D.2 The Complementary Error Function
Appendix E hspace*18mm Gamma Function
Appendix F hspace*18mm Infinite Series
F.1 Numerical Series
F.2 Trigonometric Series
Appendix G hspace*18mm The Fresnel Integrals
G.1 The Fresnel Cosine Integral
G.2 The Fresnel Sine Integral
Answers
Index
版权
