MAT-20004 - Complex Variable I and Vector Calculus
Coordinator: Anthony D Osborne Room: MAC2.13 Tel: +44 1782 7 33265
Lecture Time: See Timetable...
Level: Level 5
Credits: 15
Study Hours: 150
School Office: 01782 733075

Programme/Approved Electives for 2020/21

None

Available as a Free Standing Elective

No

Co-requisites

None

Prerequisites

None

Barred Combinations

None

Description for 2020/21

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.

Aims
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: 1,3
2,3
1,2,3
combine theoretical results to prove theorems involving vector and complex functions: 1,2,3
analyse 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:

Study hours

Lectures: 36 hours
Tutorials: 12 hours
Preparation of coursework and class tests: 12 hours
Independent study: 88 hours
Unseen examination: 2 hours


School Rules

None

Description of Module Assessment

1: Assignment weighted 15%
Online assignment on Vector Calculus
One online 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%
Online assignment
One online 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: Open Book Examination weighted 70%
Online examination - 2 hours
The examination paper will consist of no less than five and not more than eight questions, all of which are compulsory.