Complex Functions
| Code | School | Level | Credits | Semesters |
| MATH2036 | School of Mathematical Sciences | 2 | 10 | Spring China |
- Code
- MATH2036
- School
- School of Mathematical Sciences
- Level
- 2
- Credits
- 10
- Semesters
- Spring China
Summary
This module provides an introduction to the theory and applications of functions of a complex variable, using an approach oriented towards methods and applications. The elegant theory of complex functions is developed and then used to evaluate certain real integrals. Topics to be covered will include: analytic functions and singularities; series expansions; contour integrals and the calculation of residues; applications of contour integration.
Target Students
Single Honours students from the School of Mathematical Sciences.
Classes
- One 1-hour workshop each week for 12 weeks
- One 2-hour lecture each week for 12 weeks
Activities may take place every teaching week of the Semester or only in certain weeks.
Assessment
- 10% Inclass Exam 1 (Written): Inclass test
- 90% Exam 1 (2-hour): 2-hour written examination
Assessed by end of spring semester
Educational Aims
The aim of thismodule is to introduce the theory of functions of a complex variable, a topic which is very important for applications.Learning Outcomes
A student who completes this module successfully will be able to:
L1 - apply the Cauchy-Riemann equations to identify analytic functions;
L2 - compute contour integrals;
L3 - calculate Taylor and Laurent series of analytic functions;
L4 - identify singularities of analytic functions and calculate residues;
L5 - evaluate real definite integrals using residues.