Vector Calculus

The details
Mathematical Sciences
Colchester Campus
Undergraduate: Level 5
Thursday 03 October 2019
Saturday 14 December 2019
09 April 2020


Requisites for this module


MA225, MA323

Key module for

BSC L1G2 Economics and Mathematics (Including Placement Year),
BSC LG11 Economics and Mathematics,
BSC LG18 Economics and Mathematics (Including Foundation Year),
BSC LG1C Economics and Mathematics (Including Year Abroad),
BSC G100 Mathematics,
BSC G102 Mathematics (Including Year Abroad),
BSC G103 Mathematics (Including Placement Year),
BSC G104 Mathematics (Including Foundation Year),
BSC G1F3 Mathematics with Physics,
BSC G1F4 Mathematics with Physics (Including Placement Year),
BSC GCF3 Mathematics with Physics (Including Year Abroad)

Module description

This module covers the classical theory of vector calculus. Topics covered include gradient, divergence and curl, areas of surfaces and integrals over surfaces. Three central theorems of the subject, Green's Theorem, the Divergence Theorem, and Stokes' theorem, are developed and various examples are given including applications to electromagnetism and Maxwell's equations.

Module aims

To introduce the classical theory of vector calculus, including vector differential operators and line and surface integrals, and associated applications.

Module learning outcomes

On completion of the module, students should:
- Be familiar with the concept of a scalar field and a vector field and how they are related.
- Know and understand how to determine gradient, divergence, and curl, and related combinations.
- Understand how and when to apply a change of coordinates in integral problems, including polar, cylindrical, and spherical coordinates.
- Be able to determine line integrals for a scalar field and for a vector field, including the use and application of Green’s Theorem.
- Be able to determine surface integrals for a scalar field and for a vector field, including the use and application of the Divergence Theorem and Stokes’ Theorem.
- Be familiar with Maxwell’s equations and applications of vector calculus in electromagnetism.

Module information

A more detailed syllabus is as follows:
Brief review of Vectors, including scalar and cross products.
Definition of gradient, divergence and curl. Examples.
Brief review of double integrals (including change of variables), triple integrals.
Path and line integrals.
Areas of surfaces, integrals over surfaces.
Green's Theorem (sketch proof included but not examinable).
Divergence Theorem.
Stokes Theorem.
Applications and examples.
Maxwell’s equations.

Learning and teaching methods

This module consists of 30 contact hours consisting of 25 lectures and five classes. There are three revision lectures in the summer term.


  • William Cox. (May 1, 1998) Vector Calculus (Modular Mathematics Ser): Butterworth-Heinemann.
  • Vector Calculus,

The above list is indicative of the essential reading for the course. The library makes provision for all reading list items, with digital provision where possible, and these resources are shared between students. Further reading can be obtained from this module's reading list.

Assessment items, weightings and deadlines

Coursework / exam Description Deadline Weighting
Coursework   Test 1     
Coursework   Test 2     
Exam  1440 minutes during Summer (Main Period) (Main) 

Overall assessment

Coursework Exam
20% 80%


Coursework Exam
0% 100%
Module supervisor and teaching staff
Prof Edward Codling, email:
Prof Edward Codling, email
Professor Edward Codling (



External examiner

Dr Tania Clare Dunning
The University of Kent
Reader in Applied Mathematics
Available via Moodle
Of 110 hours, 30 (27.3%) hours available to students:
80 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).


Further information
Mathematical Sciences

Disclaimer: The University makes every effort to ensure that this information on its Module Directory is accurate and up-to-date. Exceptionally it can be necessary to make changes, for example to programmes, modules, facilities or fees. Examples of such reasons might include a change of law or regulatory requirements, industrial action, lack of demand, departure of key personnel, change in government policy, or withdrawal/reduction of funding. Changes to modules may for example consist of variations to the content and method of delivery or assessment of modules and other services, to discontinue modules and other services and to merge or combine modules. The University will endeavour to keep such changes to a minimum, and will also keep students informed appropriately by updating our programme specifications and module directory.

The full Procedures, Rules and Regulations of the University governing how it operates are set out in the Charter, Statutes and Ordinances and in the University Regulations, Policy and Procedures.