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

Compulsory Assignments and Attendance

Excercises

Forms of Assessment

Written examination: 5 hours

Available aids: None

Due to the measures taken to avoid the spread of SARS-CoV-2, UiB is closed for teaching and assessment. As a consequence, the following changes is made to assessment spring semester 2020:

• Grading scale ¿Pass/Fail¿ instead of ¿A-F¿
• Written home examination instead of written examination

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.