MA302-6-SP-CO:
Complex Variables and Applications

The details
2019/20
Mathematical Sciences
Colchester Campus
Spring
Undergraduate: Level 6
Current
Monday 13 January 2020
Friday 20 March 2020
15
01 October 2019

 

Requisites for this module
(none)
(none)
(none)
(none)

 

(none)

Key module for

BSC G100 Mathematics,
BSC G102 Mathematics (Including Year Abroad),
BSC G103 Mathematics (Including Placement Year),
BSC G104 Mathematics (Including Foundation Year),
BSC G1G4 Mathematics with Computing (Including Year Abroad),
BSC G1G8 Mathematics with Computing (Including Foundation Year),
BSC G1GK Mathematics with Computing,
BSC G1IK Mathematics with Computing (Including Placement Year),
BSC G1F3 Mathematics with Physics,
BSC G1F4 Mathematics with Physics (Including Placement Year),
BSC GCF3 Mathematics with Physics (Including Year Abroad)

Module description

An introduction to complex analysis, up to and including evaluation of contour integrals using the Residue theorem.

Module aims

Syllabus
- Complex numbers: Cartesian and polar forms
- Lines, circles and regions in the complex plane
- Functions of a complex variable: analytic functions
- Cauchy's theorem (statement only)
- Cauchy's integral formula
- Derivatives of an analytic function
- Taylor's theorem
- Singularities : Laurent's theorem
- Residues: calculation of residues at poles
- Cauchy's residue theorem
- Jordan's lemma
- Calculation of definite integrals using residue theory.

Module learning outcomes

On successful completion of the course, students should be able to:
- express complex numbers in both cartesian and polar forms;
- identify curves and regions in the complex plane defined by simple formulae;
- determine whether and where a function is analytic;
- obtain appropriate series expansions of functions;
- evaluate residues at pole singularities;
- apply the Residue Theorem to the calculation of real integrals.

Module information

No additional information available.

Learning and teaching methods

This course runs at 3 lectures per week. In the Summer term 3 revision lectures are given.

Bibliography

This module does not appear to have any essential texts. To see non-essential items, please refer to the module's reading list.

Assessment items, weightings and deadlines

Coursework / exam Description Deadline Weighting
Written Exam Test 1
Written Exam Test 2
Exam 120 minutes during Summer (Main Period) (Main)

Overall assessment

Coursework Exam
20% 80%

Reassessment

Coursework Exam
0% 100%
Module supervisor and teaching staff
Professor Chris Saker (cjsake@essex.ac.uk)
Professor Christopher Saker (cjsake@essex.ac.uk)

 

Availability
Yes
Yes
No

External examiner

Dr Tania Clare Dunning
The University of Kent
Reader in Applied Mathematics
Resources
Available via Moodle
Of 37 hours, 33 (89.2%) hours available to students:
4 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).

 

Further information
Mathematical Sciences

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