Module Title  Real and Complex Variable Theory 
School  Mathematics 
Department  Mathematics 
Module Code  06 22497 
Module Lead  A Sobolev 
Level  Intermediate Level 
Credits  20 
Semester  Full Term 
Prerequisites 

Corequisites 

Restrictions  none 
Contact Hours 
Lecture46 hours
Seminar0 hours
Tutorial10 hours
Project supervision0 hours
Demonstration0 hours
Practical Classes and workshops0 hours
Supervised time in studio/workshop0 hours
Fieldwork0 hours
External Visits0 hours
Work based learning0 hours
Guided independent study0 hours
Placement0 hours
Year Abroad0 hours

Exclusions  
Description  This module follows on from the second half of material in prerequisites Foundation and Abstraction 1 and 2 and gives a rigorous treatment of limits, continuity and differentiability for real functions. The material formalises and justifies many of the basic theorems and techniques of earlier modules in calculus. The module then extends to complexvalued functions, defined on regions of the complex plane, all the ideas and techniques of the integral and differential calculus which have been studied previously. 
Learning Outcomes  By the end of the module the student will be able to: understand the concepts and properties of limits, continuity and differentiability for real functions; evaluate limits and derivatives for examples involving wellknown functions; appreciate and apply theoriems concerned with continuity and differentiability (eg the Intermediate Value Theorem, the Mean Value Theorem and Taylor's Theorem); determine where a complexvalued function is analytic and identify its singular points; evaluate Taylor series and Laurent series of complexvalued functions; apply Cauchy's Integral theorem and the residue theorem to evaluate real integrals. 
Assessment 
2249701 : CA Sem 1 : Coursework (10%)
2249702 : CA Sem 2 : Coursework (10%)
2249703 : Exam : Exam (Centrally Timetabled)  Written Unseen (80%)

Assessment Methods & Exceptions  3 hr examination 80%, coursework and/or class test 20% 
Other  none 
Reading List 
