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Complex Analysis - Period 4+5
概述
CEA CAPA 合作伙伴机构: Vrije Universiteit Amsterdam
地点: Amsterdam, 荷兰
Primary Subject Area: 数学
指令: 英语
课程代码: X_400386
记录来源: 合作伙伴机构
课程详细信息: 300级
Recommended Semester Credits: 3
联系时间: 84
描述
In complex analysis one generalizes the standard concepts of real analysis such as differentiation and integration from the real line to the complex plane. Although these generalizations arise very naturally and all standard examples of functions are also differentiable in the complex sense, the latter property surprisingly turns out to be much stronger. 因此, complex differentiable functions immediately obey very special properties which we are going to explore in this course. 特别是, they lead to completely new and efficient methods for computing integrals of real functions.
During the lectures the following topics will be treated:
- complex differentiation and the Cauchy-Riemann equations
- complex integration and the theorem of Cauchy-Goursat
- elementary properties of complex differentiable functions
- singularities, Laurent series and the residue theorem
- application to integrals of real functions
联系 hours listed under a course description may vary due to the combination of lecture-based and independent work required for each course therefore, CEA's recommended credits are based on the ECTS credits assigned by VU Amsterdam. 1 ECTS equals 28 contact hours assigned by VU Amsterdam.
During the lectures the following topics will be treated:
- complex differentiation and the Cauchy-Riemann equations
- complex integration and the theorem of Cauchy-Goursat
- elementary properties of complex differentiable functions
- singularities, Laurent series and the residue theorem
- application to integrals of real functions
联系 hours listed under a course description may vary due to the combination of lecture-based and independent work required for each course therefore, CEA's recommended credits are based on the ECTS credits assigned by VU Amsterdam. 1 ECTS equals 28 contact hours assigned by VU Amsterdam.