# Functions of a Complex Variable

## Undergraduate course

- ECTS credits
- 10
- Teaching semesters
- Spring
- Course code
- MAT213
- Number of semesters
- 1
- Teaching language
- English
- Resources
- Schedule

## Course description

## Objectives and Content

Some theory of analytic functions of one complex variable, complex integrals, series of Taylor and Laurent, many-valued functions, calculus of residues.

## Learning Outcomes

After completed course, the students are expected to be able to

- Parametrize curves in the complex plane and integrate complex functions along such curves.
- Use elementary analytic functions like the exponential and logarithmic functions, trigonometric functions, polynomials and rational functions.
- Use residue calculations as integration method and find the Taylor or Laurent series of a given function.
- Attain insight in the problem of multiple solutions of the complex logarithm and the square root.
- Describe the maximum principle, Liouville's theorem and the fundamental theorem of algebra.
- Know the properties of elementary mappings such as the linear fractional transformation.

## Semester of Instruction

Spring

## Required Previous Knowledge

None

## Recommended Previous Knowledge

MAT112 Calculus II

## Credit Reduction due to Course Overlap

M113: 9 ECTS

## Compulsory Assignments and Attendance

Excercises

## Forms of Assessment

Written examination: 4 hours

Available aids: None

## Grading Scale

The grading scale used is A to F. Grade A is the highest passing grade in the grading scale, grade F is a fail.