| 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. van den Berg |
| Open unit status | Not open |
| Pre-requisites |
Level 1 Analysis, MATH 20900 Further Calculus. The unit MATH 20200, Analysis 2 is helpful but not essential. |
| Co-requisites |
None |
| School/department | School of Mathematics |
| Faculty | Faculty of Science |
Complex analysis, or the calculus of complex-valued functions, is one of the most beautiful self-contained areas of mathematics. In many ways simpler than real one-variable calculus, it is possible to derive far-reaching results having important scientific applications as well as providing powerful tools in other branches of mathematics. Starting from the idea of differentiability of complex- valued functions through the idea of conformal mappings, leading up to Cauchy's theorem on the integration of complex functions, it proves possible to tackle successfully such diverse problems as two-dimensional potential flows of an ideal fluid or to evaluate explicitly improper real integrals or infinite series.
Aims
To impart an understanding of Complex Function Theory, and facility in its application.
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 Calculus 2. Students should have a good knowledge of first year analysis and second year calculus courses.
From 2002-3 Complex Function Theory will not be required for Methods 3 or Fluid Dynamics, because Calculus 2 from 2001-2 onwards will contain enough complex function theory to support those units.
Syllabus
Exchangeability, distributions and parameters Sufficient statistics The Exponential family of distributions Model criticism and estimation The Likelihood Principle Maximum likelihood and Bayesian approaches to estimation Prediction (if time)
At the end of the unit students should:
Transferable skills:
Problem solving and logical analysis.
Lecture course of 30 lectures, with weekly exercise sheets to be done by students.
The assessment mark for Complex Function Theory 3 is calculated from a 2 ½-hour written examination in April consisting consisting of FIVE questions. A candidate's best FOUR answers will be used for assessment. Calculators of an approved type (non-programmable, no text facility) are allowed.
Many books dealing with complex analysis may be found in section QA331 of the Queen's Library. The books:
may be found particularly useful. The bulk of the course will follow [1] quite closely. The Schaum Outline Series Complex Variables by M. R. Spiegel is a good additional source of problems.
