Module information for 2004/2005
-
Credits: 10
-
Duration: approximately 22 lectures,
two lectures a week plus fortnightly problem classes
and one special examples class.
Lectures start on Monday January 24th 2005.
-
Lecturer:
Dr J. F. Feinstein, room C301 Maths/Physics,
email
Joel.Feinstein@nottingham.ac.uk
-
Lecture times: Monday 12:00 and Friday 10:00, both in Pope A13.
- Problem Classes: Fortnightly (in teaching weeks 3,5,7,9 and 11)
on Mondays 17:00, Pope A13.
-
Special examples class in teaching week 2 only:
Monday 17:00, Pope A13.
-
Office hours:
Dr J.F. Feinstein, room C301 M&P:
See the web page
http://www.maths.nott.ac.uk/personal/jff/ttnow.html
for details of Dr Feinstein's timetable and office hours.
- Module Message Board:
The module message board is available from the
Student Portal Course Homepage for G1BCOF. To find this, log in
to http://my.nottingham.ac.uk, choose
the My Teaching tab, and click on the View your modules button.
You should regularly check the Message Board topic Discussion, questions and answers.
Feel free
to post questions, answers and suggestions concerning the module there.
I will keep an eye on
this, and may well contribute my own answers if appropriate.
Answers to Frequently Asked Questions appear in the G1BCOF FAQ
document, available from the module web page at
http://www.maths.nott.ac.uk/personal/jff/G1BCOF/#handouts
- Summary of content:
This module provides an introduction to the theory and applications of
functions of a complex variable, using an approach oriented towards methods
and applications. The elegant theory of complex functions is developed and then used to
evaluate certain real integrals.
Topics to be covered will include: analytic functions and singularities; series expansions;
contour integrals and the calculation of residues; applications of contour integration.
-
Prerequisites:
Knowledge of elementary analysis, calculus of real functions, and complex
numbers, as provided by the modules G11CAL, G11ACF and G11LMA.
- Corequisites:
None
-
Module aims:
This module forms part of both the Pure Mathematics strand
and one of the Applied Mathematics strands.
The theory of functions of a complex variable is very
important for applications
as well as leading to more advanced study in the level 4 module G14COA.
-
Learning outcomes:
A student who completes this module successfully will develop a variety of
intellectual, professional and transferable skills. Such a student should also
gain the knowledge and understanding to be able to:
- identify analytic functions and their singularities;
- calculate Taylor and Laurent series;
- calculate residues of functions and compute contour integrals;
- evaluate real definite integrals using residues.
Assessment:
Assessment will be entirely by one 2-hour written examination.
There will be five questions, and your best four answers will count. If you
answer four of the questions perfectly, then you will obtain full marks.
Please note that no calculators will be permitted in the examination.
Should a resit examination be required in August/September it will
take the same form
as above (five questions, best four answers count, no calculators).
You may find it useful to look at the Spring 2003-4 exam paper for this module.
(See below for solutions to
that exam paper and comments on the students' answers to it.)
You may also find it useful to look at past exam papers
for Professor Langley's module G12CAN Complex Analysis:
solutions to the 2002/2003 paper are available from the short loan section of
the George Green Library. Note, however, that the G12CAN examinations had a
different rubric.
-
Books:
Handouts and additional documents
The following documents are currently available from the
module web page.
- Module information sheet (this document).
- Blow-by-blow account of the module, as it was given last year:
ps, pdf
- Blow-by-blow account of the module so far this year:
ps, pdf
- Frequently Asked Questions (FAQ), twelve questions
and answers so far from 2004-5 (most recent added 17/5/05),
fifteen questions and answers from 2003-4:
ps, pdf
- Full lecture notes (based on Professor Langley's notes for his module G12CAN, with very minor modifications by Dr Feinstein):
ps, pdf
- Module slides (117 slides, based on the full lecture notes above)
- 4 slides per page: ps, pdf
- 1 slide per page:
ps, pdf
- Solutions to Section 5.3, examples 3-8:
ps, pdf
- Solutions to the 2003-4 Spring Semester Examination:
ps, pdf
- Comments on students' answers to the 2003-4 Spring Semester Examination:
ps, pdf
- The Spring 2004-5 exam paper is now available from the Student Portal module page for G1BCOF
(log in to http://my.nottingham.ac.uk).
- Solutions to the G1BCOF Spring 2004-5 exam paper:
ps, pdf
Coursework (problems/exercises)
Coursework is due in at the end of the Friday lecture in weeks 2, 4,
6, 8 and 10.
It does not form part of the assessment,
but should give you useful feedback, and its completion is strongly
advised in order to master the techniques of the module. If you have any
queries about the marking of your work you should see Dr Feinstein.
Problem classes
take place in weeks 3, 5, 7, 9 and 11
and there will also be a special examples class in teaching week
2.
Solutions to all of these questions will be made available on the web as
the module progresses.
- Questions for the special examples class in teaching week 2:
ps, pdf
- Solutions to the special examples class:
ps, pdf
- Coursework and problem class questions:
ps, pdf
These questions were originally compiled by
Professor Langley for his module G12CAN Complex Analysis 2002-3.
Dr Feinstein has made very minor alterations to the questions and solutions.
- Solutions to Section 5.3, examples 3-8:
ps, pdf
- Solutions to the 2003-4 Spring Semester Examination:
ps, pdf
- Comments on students' answers to the 2003-4 Spring Semester Examination:
ps, pdf
- The Spring 2004-5 exam paper is now available from the Student Portal module page for G1BCOF, 2004-5 session.
(log in to http://my.nottingham.ac.uk).
- Solutions to the G1BCOF Spring 2004-5 exam paper:
ps, pdf