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MAT-20047 - Module Specification
School of Computer Science and Mathematics
Faculty of Natural Sciences

For academic year: 2026/27 Last Updated: 17 March 2026

MAT-20047 - Complex Variable and Vector Calculus
Coordinator:
Lecture Time: See Timetable...
Level: Level 5
Credits: 15
Study Hours: 150
School Office: 01782 733075

Programme/Approved Electives for 2026/27

None

Available as a Free Standing Elective

No

Co-requisites

None

Prerequisites

None

Barred Combinations

None

Description for 2026/27

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 variables 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: 1,2
analyse a problem involving functions of complex variables, then select and apply appropriate theoretical material and/or computational methods to solve the problem: 1,2
state and/or prove standard theorems involving vector and complex functions
: 1,2

Study hours

Lectures: 36 hours
Tutorials: 12 hours
Preparation of problem sheets: 12 hours
Independent study: 88 hours
Unseen examination: 2 hours

School Rules

None

Description of Module Assessment

1: Problem Sheets weighted 30%
A selection of problem sheets on vector calculus and complex variable functions
A set of six short problem sheets on Vector Calculus and Complex Variables, with pre-allocated space for written solutions. The mark in this component will be taken in the format of 4 best out of 6, so that some of these will effectively be formative. Students should expect to spend 12 hours on this assessment.

2: Exam weighted 70%
2-hour unseen examination
The examination paper will consist of no fewer than five and not more than eight questions, all of which are compulsory

The University undertakes a continuous review of its teaching and research provision to ensure programmes are of a high quality and changes may be made to modules where it is necessary and reasonable to do so. Please be aware that minor changes to modules, such as a change to an individual assessment, can occur up until enrolment, although we endeavour to give you as much notice as possible of any changes. Details about the circumstance in which changes are made to programmes can be found in the Student Agreement, available at: https://www.keele.ac.uk/legalgovernancecompliance/governance/actcharterstatutesordinancesandregulations/studenttermsconditions/

Last Updated: 17 March 2026