Functions of a Complex Variable

Teaching semester

Spring

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.

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.