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Dansk English

MM511: Complex Analysis (5 ECTS)

STADS: 13007301

Level
Bachelor course

Teaching period
The course is offered in the spring semester.

Teacher responsible
Email: froyshov@imada.sdu.dk

Additional teachers
szymanski@imada.sdu.dk

Timetable
Group Type Day Time Classroom Weeks Comment
Common I Monday 08-10 U156 11,13,19
Common I Monday 12-14 U156 12
Common I Monday 08-10 U154 20
Common I Monday 08-10 U51 23
Common I Tuesday 10-12 U49 10
Common I Tuesday 10-12 U156 16-18
Common I Wednesday 08-10 U154 17
Common I Thursday 10-12 U155 11
Common I Thursday 08-10 U154 22
Common I Friday 15-17 U146 12
Common I Friday 10-12 U142 20
Common I Friday 10-12 U154 22
H1 TE Monday 12-14 U154 13
H1 TE Monday 10-12 U51 23
H1 TE Tuesday 10-12 U146 11
H1 TE Tuesday 12-14 U154 20
H1 TE Wednesday 08-10 U154 16,18-19,21-22
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Comment:
Ubegrænset deltagerantal

Prerequisites:
None

Academic preconditions:
The contents of MM501 Calculus I, MM502 Calculus II, MM508 Topology I or MM533 and MM509 Topology II or FF502/ FF506/ MM529 must be known.

Course introduction
To give the students a fundamental knowledge of the theory of analytic functions, which will enable them to use this important theory in other areas of Mathematics and Applied Mathematics, as well as in problems from Physics.

Qualifications
Having completed the course successfully the students are expected:

  • to have a fundamental understanding of the theory of analytic functions and its applications.
  • to be able to use the calculation of residues to compute important types of integrals.
  • to be able to expand the most important holomorphic functions into power series and expand meromorphic functions into Laurent series.
Expected learning outcome
By the end of the course the student will be able to:

  • give an oral presentation of the statement and proofs related to any subject on a previously given list of topics within the course syllabus
  • formulate the oral presentation in a mathematically correct way
  • calculate power - and Laurent series for standard functions
  • use the residue theorem to calculate integrals • answer supplementary questions from the teacher and external examinator on definitions and results from the course syllabus
Subject overview
  • Power series, analytic functions.
  • Cauchy's integral theorem and integral formulas.
  • The fundamental theorem of algebra.
  • Taylor- and Laurent series of analytic functions.
  • Poles and zeroes. The residue theorem and its applications to compute definite integrals.
Literature
    Meddeles ved kursets start.


Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:
a) Mandatory assignments. Pass/fail, internal evaluation by teacher. the assignment must be passed in order to take the oral exam.
b) Oral exam. External marking. Marks according to the Danish 7-point scale.

Expected working hours
The teaching method is based on three phase model.

Forelæsninger (32 timer).
Eksaminatorier (18 timer).
Educational activities

Language
This course is taught in Danish or English, depending on the lecturer. However, if international students participate, the teaching language will always be English.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.