Download 2013/14 - ECM3703 - Complex Analysis Module Title Complex

2013/14 - ECM3703 - Complex Analysis
Module Title
Complex Analysis
Credit Value:
15
Module Code
ECM3703
Module Convener:
Dr Robin Chapman
(Coordinator)
DURATION: TERM
1
2
3
DURATION: Weeks
0
11 weeks
0
Number of Students Taking Module (anticipated)
47
DESCRIPTION - summary of the module content
Complex analysis is one of the most beautiful and complete theories in mathematics. Invented in the 19th century by Gauss, Cauchy
and Riemann, it has developed into a powerful tool, indispensable to all mathematicians, pure and applied. The skill of computing
integrals by means of residue calculus is a major tool in integration and it is an invaluable tool in physics and engineering. In this
module, you will see the theory developed in a logical way, emphasizing the wide range of useful applications. You will learn to develop
complex analysis in a logical and satisfying way that provides insight into the geometric and topological foundations of the subject. This
skill is useful to engineers as it helps you to understand that taking a different viewpoint may render a difficult problem easy.
Prerequisite module: ECM2701 or equivalent
AIMS - intentions of the module
The main aim of this module is to inspire a genuine engagement with complex analysis and its applications in other branches of
mathematics
INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)
On successful completion of this module, you should be able to:
Module Specific Skills and Knowledge:
1 understand basic topological concepts like connectedness;
2 comprehend the theory of holomorphic functions, their power-series and integrals;
3 compute contour integrals and to apply this to real analysis.
Discipline Specific Skills and Knowledge:
4 compute integrals by means of residue calculus which is a major tool in integration and an invaluable tool in physics, engineering etc;
5 recognise a couple of useful techniques for the computation of integrals with complex methods.
Date of Last Revision: October 9th 2013
2013/14 - ECM3703 - Complex Analysis
Personal and Key Transferable/ Employment Skills and Knowledge:
6 appreciate that taking a different viewpoint may render a difficult problem easy;
7 value the use of theoretical knowledge in concrete problems.
SYLLABUS PLAN - summary of the structure and academic content of the module)
- geometry of the complex plane;
- review of functions of a complex variable: polynomials, rational functions, elementary transcendental functions;
- open and closed sets in the complex plane, continuous curves, path connectedness, domains;
- regular functions on a domain;
- continuity, differentiability, Cauchy-Riemann equations;
- complex power series;
- radius of convergence;
- properties of power series, including differentiation within circle of convergence;
- piecewise continuously differentiable curves;
- contour integrals;
- primitives;
- existence of primitives for simply connected domains;
- Cauchy's Theorem;
- Cauchy integral formulae;
- Taylor series and Laurent series;
- isolated singularities;
- poles, removable and essential singularities;
- maximum modulus principle, Liouville's theorem, fundamental theorem of algebra, meromorphic functions, residue theorem;
- Rouche's theorem, principle of the argument;
- applications to definite integrals, summation of series and the location of zeros.
LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
Scheduled
Learning &
Teaching Activities
33.00
Date of Last Revision: October 9th 2013
Guided
Independent Study
117.00
Placement / Study
Abroad
0.00
2013/14 - ECM3703 - Complex Analysis
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
Category
Hours of study time
Description
Scheduled learning and teaching activities
33
Lectures/example classes
Guided independent study
117
Working on set mathematical problems
ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
Form of Assessment
Size of Assessment (e.g.
duration/length)
ILOs Assessed
Feedback Method
Not applicable
SUMMATIVE ASSESSMENT (% of credit)
Coursework
20
Written Exams
80
Practical Exams
Form of Assessment
% of Credit
Size of Assessment
(e.g. duration/length)
ILOs Assessed
Feedback Method
Written exam – closed
book
80
2 hours
All
Specific comments by
markers and general
comments on website
Coursework – example
sheets
20
60 hours
All
Specific comments by
markers and general
comments on website
DETAILS OF RE-ASSESSMENT (where required by referral or deferral)
Original Form of Assessment
Form of Re-assessment
ILOs Re-assessed
Time Scale for
Re-reassessment
All above
Written exam (100%)
All
August Ref/Def period
RE-ASSESSMENT NOTES
If a module is normally assessed entirely by coursework, all referred/deferred assessments will normally be by assignment.
If a module is normally assessed by examination or examination plus coursework, referred and deferred assessment will normally be
by examination. For referrals, only the examination will count, a mark of 40% being awarded if the examination is passed. For deferrals,
candidates will be awarded the higher of the deferred examination mark or the deferred examination mark combined with the original
coursework mark.
Date of Last Revision: October 9th 2013
2013/14 - ECM3703 - Complex Analysis
RESOURCES
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener
ELE – http://vle.exeter.ac.ukReading list for this module:
Author
Title
Edition
Publisher
Year
ISBN
Stewart I. & Tall D.
Complex Analysis
(the hitchhiker's
guide to the plane)
Cambridge
University Press
1983
000-0-521-28763-4
Priestley H.A.
Introduction to
Complex Analysis
Oxford University
Press
2003
000-0-198-53428-0
Howie, John M
Complex Analysis
Springer
2003
000-1-852-33733-8
Spiegel M.R.
Schaum's outline of
theory and problems
of complex variables
: with an introduction
to conformal
mapping and its
appreciation.
McGraw-Hill
1981
000-0-070-84382-1
CREDIT VALUE
15
ECTS VALUE
7.5
PRE-REQUISITE MODULES
ECM2701
CO-REQUISITE MODULES
None
NQF LEVEL (FHEQ)
3 (NQF level 6)
AVAILABLE AS DISTANCE
LEARNING
No
ORIGIN DATE
Monday 19 November 2012
LAST REVISION DATE
Wednesday 09 October 2013
KEY WORDS SEARCH
Complex analysis; contour integration; residue calculus.
Date of Last Revision: October 9th 2013