MA302-6-SP-CO:
Complex Variables and Applications
2018/19
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Spring
Undergraduate: Level 6
Current
Monday 14 January 2019
Friday 22 March 2019
15
01 April 2019
Requisites for this module
(none)
(none)
(none)
(none)
(none)
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)
An introduction to complex analysis, up to and including evaluation of contour integrals using the Residue theorem.
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.
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.
No information available.
No information available.
Available to Socrates /IP students spending all relevant terms at Essex.
This course runs at 3 lectures per week. In the Summer term 3 revision lectures are given.
This module does not appear to have a published bibliography.
Assessment items, weightings and deadlines
| Coursework / exam |
Description |
Deadline |
Coursework weighting |
| Written Exam |
Test 1 |
|
|
| Written Exam |
Test 2 |
|
|
| Exam |
Main exam: 120 minutes during Summer (Main Period)
|
Exam format definitions
- Remote, open book: Your exam will take place remotely via an online learning platform. You may refer to any physical or electronic materials during the exam.
- In-person, open book: Your exam will take place on campus under invigilation. You may refer to any physical materials such as paper study notes or a textbook during the exam. Electronic devices may not be used in the exam.
- In-person, open book (restricted): The exam will take place on campus under invigilation. You may refer only to specific physical materials such as a named textbook during the exam. Permitted materials will be specified by your department. Electronic devices may not be used in the exam.
- In-person, closed book: The exam will take place on campus under invigilation. You may not refer to any physical materials or electronic devices during the exam. There may be times when a paper dictionary,
for example, may be permitted in an otherwise closed book exam. Any exceptions will be specified by your department.
Your department will provide further guidance before your exams.
Overall assessment
Reassessment
Module supervisor and teaching staff
Dr Martin Griffiths, email: griffm@essex.ac.uk.
Dr David Penman, email dbpenman@essex.ac.uk
Miss Claire Watts, Department Manager, email cmwatts@essex.ac.uk
Yes
Yes
No
Dr Tania Clare Dunning
The University of Kent
Reader in Applied Mathematics
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).
Disclaimer: The University makes every effort to ensure that this information on its Module Directory is accurate and up-to-date. Exceptionally it can
be necessary to make changes, for example to programmes, modules, facilities or fees. Examples of such reasons might include a change of law or regulatory requirements,
industrial action, lack of demand, departure of key personnel, change in government policy, or withdrawal/reduction of funding. Changes to modules may for example consist
of variations to the content and method of delivery or assessment of modules and other services, to discontinue modules and other services and to merge or combine modules.
The University will endeavour to keep such changes to a minimum, and will also keep students informed appropriately by updating our programme specifications and module directory.
The full Procedures, Rules and Regulations of the University governing how it operates are set out in the Charter, Statutes and Ordinances and in the University Regulations, Policy and Procedures.