Functions of a Complex Variable

Undergraduate course

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

Required Previous Knowledge
Recommended Previous Knowledge
MAT112 Calculus II
Credit Reduction due to Course Overlap
M113: 9 ECTS
Compulsory Assignments and Attendance
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.