復(fù)函數(shù)論導(dǎo)論

內(nèi)容概要

　　《復(fù)函數(shù)論導(dǎo)論》是一部介紹單復(fù)變函數(shù)解析理論本科生教程，內(nèi)容體系十分嚴(yán)謹?shù)植皇ЩA(chǔ)性。本書從最基本定義開始，徐徐展開，除了微積分基本知識，沒有做任何鋪墊，深入講解復(fù)分析的觀點，可以說達到了這門學(xué)科的制高點。并且將這些主要知識點：如柯西定理，黎曼射影定理、mittag-leffler定理講述的十分明朗。本書重在強調(diào)幾何，專門有一章討論共形射影，相當(dāng)于講述復(fù)函數(shù)理論的簡明教程。每章都有大量的精選練習(xí)，從簡單直接計算到很具有啟發(fā)性思想的都具有。
　　讀者對象：數(shù)學(xué)專業(yè)的本科生，研究生和相關(guān)專業(yè)的科研人員。

作者簡介

作者：（美國）帕克（Bruce P.Palka）

書籍目錄

preface
i the complex number system
1 the algebra and geometry of complex numbers
2 exponentials and logarithms of complex numbers
3 functions of a complex variable
4 exercises for chapter i
ii the rudiments of plane topology
1 basic notation and terminology
2 continuity and limits of functions
3 connected sets
4 compact sets
5 exercises for chapter ii
iii analytic functions
1 complex derivatives
2 the cauchy-riemann equations
3 exponential and trigonometric functions
4 branches of inverse functions
5 differentiability in the real sense
6 exercises for chapter iii
iv complex integration
1 paths in the complex plane
2 integrals along paths
3 rectifiable paths
4 exercises for chapter iv
v cauchy's theorem and its consequences
1 the local cauchy theorem
2 winding numbers and the local cauchy integral formula
3 consequences of the local cauchy integral formula
4 more about logarithm and power functions
5 the global cauchy theorems
6 simply connected domains
7 homotopy and winding numbers
8 exercises for chapter v
vi harmonic functions
1 harmonic functions
2 the mean value property
3 the dirichlet problem for a disk
4 exercises for chapter vi
vii sequences and series of analytic functions
1 sequences of functions
2 infinite series
3 sequences and series of analytic functions
4 normal families
5 exercises for chapter vii
viii isolated singularities of analytic functions
1 zeros of analytic functions
2 isolated singularities
3 the residue theorem and its consequences
4 function theory on the extended plane
5 exercises for chapter viii
ix conformed mapping
1 conformal mappings
2 msbius transformations
3 paemann's mapping theorem
4 the caratheodory-osgood theorem
5 conformal mappings onto polygons
6 exercises for chapter ix
x constructing analytic functions
1 the theorem of mittag-leffier
2 the theorem of weierstrass
3 analytic continuation
4 exercises for chapter x
appendix a background on fields
1 fields
2 order in fields
appendix b winding numbers revisited
1 technical facts about winding numbers
index

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《復(fù)函數(shù)論導(dǎo)論》可供高等學(xué)校數(shù)學(xué)、物理、力學(xué)及相關(guān)專業(yè)的本科生、研究生、教師，以及相關(guān)領(lǐng)域的研究人員參考使用。

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