Group | Type | Day | Time | Classroom | Weeks | Comment |
---|---|---|---|---|---|---|
Common | I | Monday | 14-16 | U26 | 16-21 | |
Common | I | Tuesday | 12-14 | U26 | 15, 19-21 | |
Common | I | Thursday | 16-18 | U20 | 19-20 | |
Common | I | Friday | 10-12 | U20 | 15-17, 21 | |
S2 | TE | Tuesday | 10-12 | U49B | 15-22 |
22.12.2006: Hold S1 nedlagt
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