Complex Analysis
Complex Analysis
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DOI：
10.1142/9062
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发表时间：
2015-07
期刊：
影响因子：
--
通讯作者：
Arumugam et.al.
中科院分区：
文献类型：
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作者：
Arumugam et.al.
本模块将发展复变函数理论，强调其几何性质并说明一些应用。介绍内容包括复数;复变函数;序列和连续性;以及复变函数的微分。表示公式涵盖了复杂函数的积分;柯西定理和柯西积分公式;泰勒级数;和劳伦特级数。留数演算涵盖留数演算;复变函数的缠绕数和零点位置;解析延拓;欧拉的伽马函数和黎曼的zeta函数。最后，应用涵盖了共形映射，流体流动，复杂的分析动力学，朱莉娅集和曼德尔布罗特集。学生需要对本模块的真实的函数的微分和积分有一个良好的了解。
This module develops the theory of functions of a complex variable, emphasising their geometric properties and indicating some applications. Introduction covers complex numbers; complex functions; sequences and continuity; and differentiation of complex functions. Representation formulas covers integration of complex functions; Cauchy’s theorem and Cauchy’s integral formula; Taylor series; and Laurent series. Calculus of residues covers residue calculus; winding number and the location of zeros of complex functions; analytic continuation; Euler’s gamma function and Riemann’s zeta function. Finally, Applications covers conformal mappings; fluid flows; complex analytic dynamics; Julia sets; and the Mandelbrot set. Students need a sound knowledge of differentiation and integration of real functions for this module.