线性与非线性积分方程

出版时间:2011-6  出版社:高等教育出版社  作者:佤斯瓦茨  页数:639  

内容概要

  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。

作者简介

作者:(美国)佤斯瓦茨(Abdul-Majid Wazwaz)

书籍目录

part i linear integral equations
1 preliminaries
 1.1 taylor series
 1.2 ordinary differential equations
 1.3 leibnitz rule for differentiation of integrals
 1.4 reducing multiple integrals to single integrals
 1.5 laplace transform
 1.6 infinite geometric series
 references
2 introductory concepts of integral equations
 2.1 classification of integral equations
 2.2 classification of integro-differential equations
 2.3 linearity and homogeneity
 2.4 origins of integral equations
 2.5 converting ivp to volterra integral equation
 2.6 converting bvp to fredholm integral equation
 2.7 solution of an integral equation
 references
3 volterra integral equations
 3.1 introduction
 3.2 volterra integral equations of the second kind
 3.3 volterra integral equations of the first kind references
4 fredholm integral equations
 4.1 introduction
 4.2 fredholm integral equations of the second kind
 4.3 homogeneous fredholm integral equation
 4.4 fredholm integral equations of the first kind
 references
5 volterra integro-differential equations
 5.1 introduction
 5.2 volterra integro-differential equations of the second
kind
 5.3 volterra integro-differential equations of the first
kind
 references
6 fredholm integro-differential equations
 6.1 introduction
 6.2 fredholm integro-differential equations of
 the second kind
 references
7 abel's integral equation and singular integral equations
 7.1 introduction
 7.2 abel's integral equation
 7.3 the generalized abel's integral equation
 7.4 the weakly singular volterra equations
 references
8 volterra-fredholm integral equations
 8.1 introduction
 8.2 the volterra-fredholm integral equations
 8.3 the mixed volterra-fredholm integral equations
 8.4 the mixed volterra-fredholm integral equations in two
variables
 references
9 volterra-fredholm integro-differential equations
 9.1 introduction
 9.2 the volterra-fredholm integro-differential equation
 9.3 the mixed volterra-fredholm integro-differential
equations
 9.4 the mixed volterra-fredholm integro-differential equations in
two variables
 references
10 systems of volterra integral equations
 10.1 introduction
 10.2 systems of volterra integral equations of the second
kind
 10.3 systems of volterra integral equations of the first
kind
 10.4 systems of volterra integro-differential equations
 references
11 systems of fredholm integral equations
 11.1 introduction
 11.2 systems of fredholm integral equations
 11.3 systems of fredholm integro-differential equations
 references
12 systems of singular integral equations
 12.1 introduction
 12.2 systems of generalized abel integral equations
 12.3 systems of the weakly singular volterra integral
equations
 references
 part ii nonlinear integral equations
13 nonlinear volterra integral equations
 13.1 introduction
 13.2 existence of the solution for nonlinear volterra integral
equations
 13.3 nonlinear volterra integral equations of the second
kind
 13.4 nonlinear volterra integral equations of the first kind
 13.5 systems of nonlinear volterra integral equations
 references
14 nonlinear volterra integro-differential equations
 14.1 introduction
 14.2 nonlinear volterra integro-differential equations of the
second kind
 14.3 nonlinear volterra integro-differential equations of the
first kind
 14.4 systems of nonlinear volterra integro-differential
equations
 references
15 nonlinear fredholm integral equations
 15.1 introduction
 15.2 existence of the solution for nonlinear fredholm integral
equations
 15.3 nonlinear fredholm integral equations of the second
kind
 15.4 homogeneous nonlinear fredholm integral equations
 15.5 nonlinear fredholm integral equations of the first kind
 15.6 systems of nonlinear fredholm integral equations
 references
16 nonlinear fredholm integro-differential equations
 16.1 introduction
 16.2 nonlinear fredholm integro-differential equations.
 16.3 homogeneous nonlinear fredholm integro-differential
equations
 16.4 systems of nonlinear fredholm integro-differential
equations
 references
17 nonlinear singular integral equations
 17.1 introduction
 17.2 nonlinear abel's integral equation
 17.3 the generalized nonlinear abel equation
 17.4 the nonlinear weakly-singular volterra equations
 17.5 systems of nonlinear weakly-singular volterra integral
equations
 references
18 applications of integral equations
 18.1 introduction
 18.2 volterra's population model
 18.3 integral equations with logarithmic kernels
 18.4 the fresnel integrals
 18.5 the thomas-fermi equation
 18.6 heat transfer and heat radiation
 references
appendix a 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 integrals involving irrational algebraic functions
 b.1 integrals involving n is an integer, n ≥ 0
 b.2 integrals involving n is an odd integer, n ≥ i
appendix c 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 the error and the complementary error
 functions
 d.1 the error function
 d.2 the complementary error function
appendix e gamma function
appendix f infinite series
 f.1 numerical series
 f.2 trigonometric series
appendix g the fresnel integrals
 g.1 the fresnel cosine integral
 g.2 the fresnel sine integral
answers
index

章节摘录

版权页:插图:Integral equations and in tegro-differential equations will be classified in to distinct types according to the limits of integration and the kernel K(x, t).Alltypes of integral equations and in tegro differential equations will be classifiedand investigated in the forthcoming chapters.   In this chapter, we will review the most important concepts needed to study integral equations. The traditional methods, such as Taylor seriesmethod and the Laplace transform method, will be used in this text. More-over, the recently developed methods, that will be used thoroughly in this text, will determine the solution in a power series that will converge to an exact solution if such a solution exists. However, if exact solution does not exist, we use as many terms of the obtained series for numerical purposes to approximate the solution.

编辑推荐

《线性与非线性积分方程:方法及应用》:关键词:线性与非线性Volterra方程,线性与非线性Fredholm方程,线性与非线性奇异方程,积分方程组。Nonlinear Physical Science focuses on the recent a dvances of fundamental theories and principles, analytical and symbolic approaches, as well as computational techniques in nonlinear physical science and nonlinear mathematics with engineering applications.

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用户评论 (总计1条)

 
 

  •   书写的理论性不强,语句啰嗦重复。但是对初学者而言,很实用,可以照猫画虎,直接套用方法。适合自学,或作为工具手册。
 

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