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## Complex Analysis

2019-2020

### Course Objective

- The student can decide whether a complex function is analytic (=
differentiable in the complex sense) and knows the connection with the
Cauchy-Riemann equations.
- She can do computations with elementary functions such as
exp/log/sin/cos over the complex numberts.
- She can integrate analytic functions along a path on the complex
plane, using the theorem of Cauchy-Goursat and its corollaries.
- She can compute Laurent series and determine the type of singularities
of analytic functions.
- She can compute integrals of complex functions using the residue
theorem and knows how to use this to compute integrals of real
functions.

### Course Content

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

### Teaching Methods

Lecture (2 hours) and tutorial class (2 hours)

### Method of Assessment

Two written exams (40%+40%) and two hand-in homeworks (10%+10%). The
retake exam counts for 100% of the final grade.

### Literature

Churchill, R. V., & Brown, J. W.: Complex variables and applications.
Ninth edition, 2014, McGraw-Hill Book Co., New York

### Target Audience

Bachelor Mathematics Year 2

### Recommended background knowledge

Calculus, Analysis, Linear algebra

### General Information

Course Code X_400386 6 EC P4+5 300 English Faculty of Science dr. O. Fabert dr. O. Fabert dr. O. Fabert

### Practical Information

You need to register for this course yourself

Last-minute registration is available for this course.

Teaching Methods Seminar, Lecture
Target audiences

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