Analysis on the Real Line II (MA1124)
Module MA2328: Complex Analysis I
- Credit weighting (ECTS)
- Semester/term taught
Hilary term 2015-16
- Contact Hours
11 weeks, 3 lectures per week
- Prof. Dmitri Zaitsev
- 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
and elliptic 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
- Elliptic functions
or Analysis in Several Real Variables (MA2321)
This module will be examined in a 2 hour examination in Trinity term.