Unit name | Complex Function Theory |
---|---|
Unit code | MATH33000 |
Credit points | 20 |
Level of study | H/6 |
Teaching block(s) |
Teaching Block 1 (weeks 1 - 12) |
Unit director | Professor. Grava |
Open unit status | Not open |
Pre-requisites |
MATH20006 Metric Spaces |
Co-requisites |
None |
School/department | School of Mathematics |
Faculty | Faculty of Science |
Unit Aims
To impart an understanding of Complex Function Theory, and facility in its application.
Unit Description
Complex function theory is a remarkably beautiful piece of pure mathematics, and at the same time an indispensable tool in number theory and in many fields of applied mathematics and mathematical methods.
Of central interest are mappings of the complex plane into itself which are differentiable. The property of differentiability alone is enough to guarantee that the function can be represented locally in a power series, in stark contrast to the real-variable theory. This shows that complex analysis is in some ways simpler than real analysis.
The integration theory for complex differentiable functions is highly geometric in nature. Moreover, it provides powerful tools for evaluating real integrals and series. The logarithm and square-root functions on the complex plane are multiple-valued; we shall briefly indicate how they can be seen as single-valued when considered to live on the associated Riemann surface.
The theory of conformal transformations is of great importance in the geometrical theory of differential equations, and has interesting applications in potential theory and fluid dynamics; we shall outline the beginnings of these.
Relation to Other Units
This unit aims for rigorous development and extension of material which has been introduced in the complex function theory part of Multivariable Calculus and Methods of Complex Functions.
At the end of the unit students should:
Transferable skills:
Problem solving and logical analysis.
The unit will be taught through a combination of
90% Timed, open-book examination 10% Coursework
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.
Recommended
Further