MAU34208 Topics in complex analysis II
| Module Code | MAU34208 |
|---|---|
| Module Title | Topics in complex analysis II |
| Semester taught | Semester 2 |
| ECTS Credits | 5 |
| Module Lecturer | Prof. Andreea Nicoara |
| Module Prerequisites | MAU34205 Topics in complex analysis I |
Assessment Details
- This module is examined in a 2-hour examination at the end of Semester 2.
- Continuous assessment contributes 20% towards the overall mark.
- Re-assessment, if needed, consists of 100% exam.
Contact Hours
11 weeks of teaching with 3 lectures per week.
Learning Outcomes
On successful completion of this module, students will be able to
- Give definitions, proofs, examples and counterexamples related to concepts covered in the module.
- Describe properties of harmonic functions and special functions such as the Gamma function and the Riemann zeta function.
- Work with linear fractional transformations and the Riemann sphere.
- Construct meromorphic functions with prescribed zeros and poles as well as elementary Riemann surfaces.
Module Content
- Singularities, Casorati-Weierstrass theorem, elementary value distribution theory, Picard theorems.
- Harmonic functions and the Dirichlet problem.
- Stereographic projection and the Riemann sphere.
- Linear fractional transformations.
- Boundary behaviour of the Riemann map.
- Divisors, Mittag-Leffler theorem, infinite products, Weierstrass theorem on canonical products.
- Gamma function, Riemann zeta function, statement of Riemann hypothesis.