Materials available from this web page (lecture notes, problem sheets etc.) are copyright © J.F. Feinstein unless otherwise stated.
G1BCOF: COMPLEX FUNCTIONS
2004/2005
URL: http://www.maths.nott.ac.uk/personal/jff/G1BCOF/index.html
Last modified: September 13 2005
See below for
 Module Information
 Handouts and additional documents
 Coursework (and solutions so far)
 Miscellaneous links of interest
Corrections, room changes etc. will be announced on 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 check this page regularly for announcements and to read the module Message Board (see below).
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.

Books:
Author Title Comments Brown, James Ward; Churchill, Ruel V. Complex variables and applications Recommended Spiegel, Murray Schaum's Outline of Complex Variables Recommended Apostol, Tom M. Mathematical Analysis More advanced
Handouts and additional documents
The following documents are currently available from the module web page.
 Module information sheet (this document).
 Blowbyblow account of the module, as it was given last year: ps, pdf
 Blowbyblow account of the module so far this year: ps, pdf
 Frequently Asked Questions (FAQ), twelve questions and answers so far from 20045 (most recent added 17/5/05), fifteen questions and answers from 20034: 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)
 Solutions to Section 5.3, examples 38: ps, pdf
 Solutions to the 20034 Spring Semester Examination: ps, pdf
 Comments on students' answers to the 20034 Spring Semester Examination: ps, pdf
 The Spring 20045 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 20045 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 20023. Dr Feinstein has made very minor alterations to the questions and solutions.  Solutions to Section 5.3, examples 38: ps, pdf
 Solutions to the 20034 Spring Semester Examination: ps, pdf
 Comments on students' answers to the 20034 Spring Semester Examination: ps, pdf
 The Spring 20045 exam paper is now available from the Student Portal module page for G1BCOF, 20045 session. (log in to http://my.nottingham.ac.uk).
 Solutions to the G1BCOF Spring 20045 exam paper: ps, pdf
Miscellaneous links which may be of interest:
 Catalogue of Modules, entry for G1BCOF: COMPLEX FUNCTIONS
 School of Mathematical Sciences Module Information
 Information Gateway, including past exam papers etc.
 Courses Office, examination information
 The University of Nottingham, Library Services (including the online catalogue)
 Blackwell's online bookshop
 Timetable, School of Mathematical Sciences
 University Study Support Centre
 Joel Feinstein's timetable
 Joel Feinstein's recommended mathematics books
 Other useful web pages.
Page maintained by Joel Feinstein, Joel.Feinstein@nottingham.ac.uk, http://explainingmaths.wordpress.com