| Unit name | Methods of Complex Functions |
|---|---|
| Unit code | MATH20001 |
| Credit points | 10 |
| Level of study | I/5 |
| Teaching block(s) |
Teaching Block 1B (weeks 7 - 12) |
| Unit director | Dr. Wiesner |
| Open unit status | Not open |
| Pre-requisites |
Analysis 1, Linear Algebra & Geometry 1 & Calculus 1 |
| Co-requisites |
None |
| School/department | School of Mathematics |
| Faculty | Faculty of Science |
Aims
The unit gives an overview over methods for differentiating and integrating complex-valued functions, introduces the underlying theoretical results, and shows how they can be applied to problems in complex and real analysis.
Description
The unit introduces functions of a complex variable, with a focus on holomorphic functions. It extends elementary calculus to functions of a complex variable, showing similarities and differences between the properties of two-dimensional vector fields and functions of a complex variable. The emphasis is on basic ideas and methods; theorems will be stated rigorously and the theory will be carefully developed, tut the emphasis is on methods rather than proofs.
Further information is available at: http://www.maths.bris.ac.uk/study/undergrad/
Be familiar with and able to use the elementary properties of holomorphic functions of a complex variable. Find power series expansions, integrate holomorphic and functions with and without singularities. Master residue calculus and apply it to real-valued integrals.
Lectures, problem sessions, homework problems and solutions
100% examination
Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.
If you fail this unit and are required to resit, reassessment is by a written examination in the August/September Resit and Supplementary exam period.
Functions of a complex variable: Jerrold E. Marsden & Michael J. Hoffman Basic Complex Analysis, Edition 3, W. H. Freeman & Company, 1999
