Programme/Approved Electives for 2023/24
Available as a Free Standing Elective
This module contains a first course on vector calculus and a first course in functions of a complex variable. The topics covered include complex functions, differentiation and integration, Cauchy's Theorems, Taylor and Laurent Series, singularities, the Residue Theorem, differentiation of vectors, differential operators, line, volume and surface integrals, Green's Theorem, the Divergence Theorem and Stokes' Theorem.Complex variable leads to elegant results in pure mathematics and both complex variable and vector calculus provide a framework for solving physical and geometrical problems.
The aim of this module is to introduce the core subjects of vector calculus and complex variable and to provide some of their many and varied applications.
Intended Learning Outcomes
analyse a problem involving vector functions, then select and apply appropriate theoretical material and/or computational methods to solve the problem: 1,32,31,2,3combine theoretical results to prove theorems involving vector and complex functions: 3analyse a problem involving complex functions, then select and apply appropriate theoretical material and/or computational methods to solve the problem: state and/or prove standard theorems involving vector and complex functions:
Lectures: 36 hoursTutorials: 12 hoursPreparation of coursework assignments: 12 hoursIndependent study: 88 hoursUnseen examination: 2 hours
1: Assignment weighted 15%
Description of Module Assessment
Take-home assignment on Vector CalculusAn assignment, containing a set of questions on Vector Calculus, with pre-allocated space for written solutions. Students should expect to spend 6 hours on this assignment.¿
2: Assignment weighted 15%
Take-home assignment on complex functionsAn assignment, containing a set of questions on Complex Variable, with pre-allocated space for written solutions. Students should expect to spend 6 hours on this assignment.¿3: Unseen Exam weighted 70%
2-hour unseen examinationThe examination paper will consist of no less than five and not more than eight questions, all of which are compulsory.