线性与非线性积分方程

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

　　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。