# Module MA23204: Introduction to Complex Analysis

**Credit weighting (ECTS)**- 5 credits
**Semester/term taught**- Hilary term 2019-20
**Contact Hours**- 11 weeks, 3 lectures per week
**Lecturer**- Prof. Marius de Leeuw
**Learning Outcomes**- On successful completion of this module, students will be able to:
- Use basic theorems on complex sequences and series, with a particular emphasis on power series. Calculate coefficients and radii of convergence of power series using these theorems.
- Demonstrate a familiarity with the basic properties of analytic functions. Apply these theorems to simple examples.
- State correctly the theorems of Cauchy and Morera. Calculate, using Cauchy's theorem and its corollaries, the values of contour integrals.
- Prove and apply properties of important examples of analytic functions, including rational functions, the exponentential and logarithmic functions, trigonometric and hyperbolic functions.

**Module Content**- Aims to introduce complex variable theory and reach the residue theorem, applications of that to integral evaluation.
- Power series
- Analytic functions
- Complex Integration
- Residue calculus

**Module Prerequisite**

**Assessment Detail**

**examination**in Trinity term.

**Continuous assessment**will contribute 15% to the final grade for the module at the annual examination session, with the examination counting for the remaining 85%. Re-assessments if required will consist of 100% exam.