## MA3CA2-Complex Analysis II

Module Provider: Mathematics and Statistics
Number of credits: 10 [5 ECTS credits]
Level:6
Terms in which taught: Spring term module
Pre-requisites: MA2CA1 Complex Analysis I
Non-modular pre-requisites:
Co-requisites:
Modules excluded:
Module version for: 2016/7

Module Convenor: Dr Horatio Boedihardjo

Summary module description:
This module continues the study of functions of one complex variable.

Aims:
To continue the study of functions of one complex variable, and in particular of analyticity and its consequences

Assessable learning outcomes:
By the end of the module, students are expected to be able to:
- Identify different type of singularities of complex functions
- Use residue calculus to study zeros and poles of given functions
- Use residues to compute complex and real integrals
- Use Rouche's Theorem to estimate the number of zeros of complex functions in regions of the complex plane.

The use of complex analytic arguments to derive basic results in algebra and real analysis

Outline content:
Starting from Cauchy’s theorem and its consequences, discussed in the prerequisite complex analysis module (MA2CA1), the module will present further properties of sequences and series of complex functions, and singularities of complex functions, leading to the concept of analytic continuation.
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 100.00 Total hours for module 100.00

Summative Assessment Methods:
 Method Percentage Written exam 100

Other information on summative assessment:
One examination paper.

Formative assessment methods:
Problem sheets.

Penalties for late submission:
The Module Convenor will apply the following penalties for work submitted late, in accordance with the University policy.

• where the piece of work is submitted up to one calendar week after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for the piece of work will be deducted from the mark for each working day (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.

Length of examination:
2 hours

Requirements for a pass:
A mark of 40% overall.

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