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Complex Analysis - Period 4+5 Social Sciences & Humanities Program Spring 2025 Semester - Amsterdam

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Complex Analysis - Period 4+5

Complex Analysis - Period 4+5 Course Overview


CEA CAPA Partner Institution: Vrije Universiteit Amsterdam
Location: Amsterdam, Netherlands
Primary Subject Area: Mathematics
Instruction in: English
Course Code: X_400386
Transcript Source: Partner Institution
Course Details: Level 300
Recommended Semester Credits: 3
Contact Hours: 84


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. As a consequence, complex differentiable functions immediately obey very special properties which we are going to explore in this course. In particular, 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

Contact 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.

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