Complex Variable (U01618)

? Credit Points : 10 ? SCQF Level : 10 ? Acronym : MAT-3-CoV

Course for Honours Degrees in Chemical Physics, Mathematical Physics and Physics. Syllabus summary: Analytic functions, contour integrals, Laurent series and residues, Fourier transform.

Entry Requirements

? Pre-requisites : (Passes at C or better in MAT-2-FoC, MAT-2-SVC, MAT-2-LiA, MAT-2-MAM) or (MAT-2-am3, MAT-2-mm3, MAT-2-am4, MAT-2-mm4 with permission of the Head of School) or (MAT-2-mi3, MAT-2-mi4 with permission of Head of School)

? Prohibited combinations : MAT-3-CVD, MAT-3-CVD0

Subject Areas

Home subject area

Specialist Mathematics & Statistics (Honours), (School of Mathematics, Schedule P)

Delivery Information

? Normal year taken : 3rd year

? Delivery Period : Semester 2 (Blocks 3-4)

? Contact Teaching Time : 2 hour(s) 30 minutes per week for 11 weeks

First Class Information

Date	Start	End	Room	Area	Additional Information
22/09/2008	12:10	13:00	Lecture Theatre B, JCMB	KB

All of the following classes

Type	Day	Start	End	Area
Lecture	Monday	12:10	13:00	KB
Lecture	Thursday	12:10	13:00	KB

Summary of Intended Learning Outcomes

1. Knowledge of basic properties of analytic functions of a complex variable, including power-series expansions, Laurent expansions, and Liouville's theorem
2. The idea of conformal mapping, use of fractional linear transformations
3. Knowledge of the fundamental integral theorems of complex analysis
4. Ability to use residue calculus to perform definite integrals
5. Knowledge of some of the relations between analytic functions and PDE, e.g. relation to harmonic functions, the maximum principle
6. Familiarity with the Fourier integral as a tool for the study of ordinary and partial differential equations.