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Undergraduate course

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 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

Compulsory Assignments and Attendance

Excercises

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.

Contact

Contact Information

advice@math.uib.no

Exam information

  • For written exams, please note that the start time may change from 09:00 to 15:00 or vice versa until 14 days prior to the exam. The exam location will be published 14 days prior to the exam.

  • Type of assessment: Written examination

    Date
    08.06.2018, 09:00
    Duration
    5 hours
    Withdrawal deadline
    25.05.2018