线性与非线性积分方程

线性与非线性积分方程

(美) 佤斯瓦茨 (Wazwaz,A.M.) , 著

出版社:高等教育出版社

年代:2011

定价:128.0

书籍简介:

本书是目前第一本同时介绍线性与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系统、深入地处理;第二部分主要处理非线性方程及其应用,并提供了对不适定Fredholm问题、分歧点、奇异点的系统的易于理解的处理方法。本书通过大量的例子讲述线性方程与非线性方程最新发展起来的高效的技术与方法而无须要求读者对抽象的理论本身有深度的理解,同时也讨论了经典的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选择自己所需的可行的、高效的方法。本书还提供大量的习题,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硕士生教材,也可供相关领域的工程师参考。

书籍目录:

part i linear integral equations1 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 references2 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 references3 volterra integral equations 3.1 introduction 3.2 volterra integral equations of the second kind 3.3 volterra integral equations of the first kind references4 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 references5 volterra integro-differential equations 5.1 introduction 5.2 volterra integro-differential equations of the secondkind 5.3 volterra integro-differential equations of the firstkind references6 fredholm integro-differential equations 6.1 introduction 6.2 fredholm integro-differential equations of the second kind references7 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 references8 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 twovariables references9 volterra-fredholm integro-differential equations 9.1 introduction 9.2 the volterra-fredholm integro-differential equation 9.3 the mixed volterra-fredholm integro-differentialequations 9.4 the mixed volterra-fredholm integro-differential equations intwo variables references10 systems of volterra integral equations 10.1 introduction 10.2 systems of volterra integral equations of the secondkind 10.3 systems of volterra integral equations of the firstkind 10.4 systems of volterra integro-differential equations references11 systems of fredholm integral equations 11.1 introduction 11.2 systems of fredholm integral equations 11.3 systems of fredholm integro-differential equations references12 systems of singular integral equations 12.1 introduction 12.2 systems of generalized abel integral equations 12.3 systems of the weakly singular volterra integralequations references part ii nonlinear integral equations13 nonlinear volterra integral equations 13.1 introduction 13.2 existence of the solution for nonlinear volterra integralequations 13.3 nonlinear volterra integral equations of the secondkind 13.4 nonlinear volterra integral equations of the first kind 13.5 systems of nonlinear volterra integral equations references14 nonlinear volterra integro-differential equations 14.1 introduction 14.2 nonlinear volterra integro-differential equations of thesecond kind 14.3 nonlinear volterra integro-differential equations of thefirst kind 14.4 systems of nonlinear volterra integro-differentialequations references15 nonlinear fredholm integral equations 15.1 introduction 15.2 existence of the solution for nonlinear fredholm integralequations 15.3 nonlinear fredholm integral equations of the secondkind 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 references16 nonlinear fredholm integro-differential equations 16.1 introduction 16.2 nonlinear fredholm integro-differential equations. 16.3 homogeneous nonlinear fredholm integro-differentialequations 16.4 systems of nonlinear fredholm integro-differentialequations references17 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 integralequations references18 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 referencesappendix 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 formsappendix 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 ≥ iappendix 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 functionsappendix d the error and the complementary error functions d.1 the error function d.2 the complementary error functionappendix e gamma functionappendix f infinite series f.1 numerical series f.2 trigonometric seriesappendix g the fresnel integrals g.1 the fresnel cosine integral g.2 the fresnel sine integralanswersindex

内容摘要:

  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。

书籍规格:

书籍详细信息
书名线性与非线性积分方程站内查询相似图书
丛书名非线性物理科学
9787040316940
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出版地北京出版单位高等教育出版社
版次1版印次1
定价(元)128.0语种英文
尺寸24 × 16装帧精装
页数印数 1200

书籍信息归属:

线性与非线性积分方程是高等教育出版社于2011.6出版的中图分类号为 O175.5 的主题关于 线性积分方程-英文 ,非线性积分方程-英文 的书籍。