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Undergraduate course

Functions of a Complex Variable

  • ECTS credits10
  • Teaching semesterSpring
  • Course codeMAT213
  • Number of semesters1
  • LanguageEnglish
  • Resources

Semester of Instruction

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 algorithm 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

NoneĀ 

Recommended Previous Knowledge

MAT112 Calculus II

Forms of Assessment

Written examination: 5 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.

Exam information