MM511: Complex Analysis (5 ECTS)

STADS: 13007301

Level
Bachelor course

Teaching period
The course is offered in the spring semester.
4th quarter.

Teacher responsible
Email: szymanski@imada.sdu.dk

Timetable
Show entire timetable
Show personal time table for this course.

Comment:
Ubegrænset deltagerantal. 4. kvartal.

Prerequisites:
None

Academic preconditions:
The contents of MM501 Calculus I, MM502 Calculus II, MM508 Topology I and MM509 Topology II 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. .

Syllabus
See syllabus.

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.