MAU23204 Introduction to complex analysis
| Module Code | MAU23204 |
|---|---|
| Module Title | Introduction to complex analysis |
| Semester taught | Semester 2 |
| ECTS Credits | 5 |
| Module Lecturer | Prof. Dmitri Zaitsev |
| Module Prerequisites |
MAU11204 Analysis on the real line OR
MAU23203 Analysis in several real variables |
Assessment Details
- This module is examined in a 2-hour examination at the end of Semester 2.
- Students are assessed based on the exam alone.
- 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
- Apply basic theorems on complex sequences and series, with a special emphasis on power series.
- Use these theorems to calculate coefficients and radii of convergence of power series.
- State basic properties of analytic functions and apply known theorems to simple examples.
- State Cauchy's theorems and use them to compute contour integrals.
- Prove and use properties of important examples of analytic functions, including rational, exponential, logarithmic, trigonometric and hyperbolic functions.
Module Content
- Analytic functions
- Complex integration
- Power series
- Residue calculus