复函数论导论

出版社: 世界图书出版公司
作者:(美)帕克
出版日期:2012-06-01
版次:1
印次:1
开本:7
内容提要:
导语: 《复函数论导论》由帕克所著，是一部介绍单复变函数解析理论本科生教程，内容体系十分严谨但又不失基础性。本书从最基本定义开始，徐徐展开，除了微积分基本知识，没有做任何铺垫，深入讲解复分析的观点，可以说达到了这门学科的制高点。并且将这些主要知识点：如柯西定理，黎曼射影定理、mittag-leffler定理讲述的十分明朗。本书重在强调几何，专门有一章讨论共形射影，相当于讲述复函数理论的简明教程。每章都有大量的精选练习，从简单直接计算到很具有启发性思想的都具有。 读者对象：数学专业的本科生，研究生和相关专业的科研人员。
目录:prefacei the complex number system1 the algebra and geometry of complex numbers2 exponentials and logarithms of complex numbers3 functions of a complex variable4 exercises for chapter iii the rudiments of plane topology1 basic notation and terminology2 continuity and limits of functions3 connected sets4 compact sets5 exercises for chapter iiiii analytic functions1 complex derivatives2 the cauchy-riemann equations3 exponential and trigonometric functions4 branches of inverse functions5 differentiability in the real sense6 exercises for chapter iiiiv complex integration1 paths in the complex plane2 integrals along paths3 rectifiable paths4 exercises for chapter ivv cauchy's theorem and its consequences1 the local cauchy theorem2 winding numbers and the local cauchy integral formula3 consequences of the local cauchy integral formula4 more about logarithm and power functions5 the global cauchy theorems6 simply connected domains7 homotopy and winding numbers8 exercises for chapter vvi harmonic functions1 harmonic functions2 the mean value property3 the dirichlet problem for a disk4 exercises for chapter vivii sequences and series of analytic functions1 sequences of functions2 infinite series3 sequences and series of analytic functions4 normal families5 exercises for chapter viiviii isolated singularities of analytic functions1 zeros of analytic functions2 isolated singularities3 the residue theorem and its consequences4 function theory on the extended plane5 exercises for chapter viiiix conformed mapping1 conformal mappings2 msbius transformations3 paemann's mapping theorem4 the caratheodory-osgood theorem5 conformal mappings onto polygons6 exercises for chapter ixx constructing analytic functions1 the theorem of mittag-leffier2 the theorem of weierstrass3 analytic continuation4 exercises for chapter xappendix a background on fields1 fields2 order in fieldsappendix b winding numbers revisited1 technical facts about winding numbersindex

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