## MA4CA2-Complex Analysis II

Module Provider: Mathematics and Statistics
Number of credits: 10 [5 ECTS credits]
Level:7
Terms in which taught: Spring term module
Pre-requisites: MA2RCA Real and Complex Analysis or MA3RCA Real and Complex Analysis
Non-modular pre-requisites:
Co-requisites:
Modules excluded: MA3CA2 Complex Analysis II
Current from: 2019/0

Module Convenor: Dr Horatio Boedihardjo

Type of module:

Summary module description:

This module continues the study of functions of one complex variable.

Aims:

To study more advanced properties of functions of one complex variable and their applications in other areas of mathematics.

Assessable learning outcomes:

By the end of the module, students are expected to be able to:

• Understand the proof of Cauchy’s theorem and integral formula, and use them to obtain further results in complex analysis;

• Use residue calculus to study properties of functions and evaluate integrals;

• Understand the basic geometric properties of Möbius transformations and their importance in complex analysis and applications;

• State and prove a selection of the main theorems;

• Use the main results to treat further problems in complex analysis and its applications.

This module will be assessed to a greater depth than the excluded module MA3CA2.

The use of complex analysis to obtain results in other parts of mathematics.

Outline content:

Cauchy’s theorem and integral formula, and their consequences; series of complex functions; residue calculus; analytic continuation; Möbius transformations; special functions; harmonic functions; applications of complex analysis.

More advanced consequences of residue calculus, such as the maximum modulus, argument principle and Rouche’s theorem, will be presented.

Brief description of teaching and learning methods:

Lectures supported by problem sheets.

Contact hours:
 Autumn Spring Summer Lectures 20 Guided independent study: 80 Total hours by term 0 100 0 Total hours for module 100

Summative Assessment Methods:
 Method Percentage Written exam 100

Summative assessment- Examinations:

2 hours.

Summative assessment- Coursework and in-class tests:

Formative assessment methods:

Problem sheets.

Penalties for late submission:
The Module Convener will apply the following penalties for work submitted late:

• where the piece of work is submitted after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for that piece of work will be deducted from the mark for each working day[1] (or part thereof) following the deadline up to a total of five working days;
• where the piece of work is submitted more than five working days after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.

• The University policy statement on penalties for late submission can be found at: http://www.reading.ac.uk/web/FILES/qualitysupport/penaltiesforlatesubmission.pdf
You are strongly advised to ensure that coursework is submitted by the relevant deadline. You should note that it is advisable to submit work in an unfinished state rather than to fail to submit any work.

Assessment requirements for a pass:

A mark of 50% overall.

Reassessment arrangements:

One examination paper of two hours duration in August/September.