Mathematical Analysis (MAT310)
The course covers fundamentals of mathematical analysis with focus on complex analysis.
Course description for study year 2024-2025. Please note that changes may occur.
Course code
MAT310
Version
1
Credits (ECTS)
10
Semester tution start
Autumn
Number of semesters
1
Exam semester
Autumn
Language of instruction
English
Content
NB! This is an elective course and may be cancelled if fewer than 10 students are enrolled by August 20th for the autumn semester.
Elements of mathematical logic, basic topological notions, analytic and harmonic functions of a complex variable, Cauchy-Riemann conditions, Cauchy's integral theorem and integral formulas, Taylor and Laurent series representations, classification of isolated singularities and residue theory.
Learning outcome
Upon completing this course students should be able to:
- Clearly understand what is meant by a mathematical proof, and how to communicate mathematical arguments clearly in the form of a mathematical proof.
- Understand basic topological notions (closed, open, connected and compact sets, convergence, continuity).
- Get operational knowledge of analytic and harmonic functions, including maximum principle and integral representations.
- Determine Taylor and Laurent series of elementary analytic functions, find their zero points and singularities, and get knowledge of residue theory and its applications.
Required prerequisite knowledge
Recommended prerequisites
Exam
| Form of assessment | Weight | Duration | Marks | Aid |
|---|---|---|---|---|
| Written exam | 1/1 | 4 Hours | Letter grades | No printed or written materials are allowed. Approved basic calculator allowed |
Written exam is with pen and paper.
Course teacher(s)
Course coordinator:
Helge Paul RuddatHead of Department:
Bjørn Henrik AuestadMethod of work
Overlapping courses
| Course | Reduction (SP) |
|---|---|
| Mathematical Analysis (BMA100_1) | 5 |
| Mathematics 5 - Complex analysis (ÅMA310_1) | 5 |