## MA210-5-AU-CO:Vector Calculus

The details
2024/25
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Autumn
Current
Thursday 03 October 2024
Friday 13 December 2024
15
04 January 2024

Requisites for this module
(none)
(none)
(none)
(none)

MA222, MA225, MA323

## Key module for

BSC G100 Mathematics,
BSC G102 Mathematics (Including Year Abroad),
BSC G103 Mathematics (Including Placement Year),
BSC G104 Mathematics (Including Foundation Year),
MMATG198 Mathematics,
BSC G1F3 Mathematics with Physics,
BSC G1F4 Mathematics with Physics (Including Placement Year),
BSC G1F5 Mathematics with Physics (Including Foundation Year),
BSC GCF3 Mathematics with Physics (Including Year Abroad),
MSCIG199 Mathematics and Data Science

## 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

The aims of this module are:

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

## Module learning outcomes

By the end of the module, students will be expected to:

1. Be familiar with the concept of a scalar field and a vector field and how they are related.

2. Know and understand how to determine gradient, divergence, and curl, and related combinations.

3. Understand how and when to apply a change of coordinates in integral problems, including polar, cylindrical, and spherical coordinates.

4. Be able to determine line integrals for a scalar field and for a vector field, including the use and application of Green’s Theorem.

5. 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.

6. Be familiar with Maxwell’s equations and applications of vector calculus in electromagnetism.

## Module information

Indicative syllabus:

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

Teaching in the School will be delivered using a range of face-to-face lectures, classes, and lab sessions as appropriate for each module. Modules may also include online only sessions where it is advantageous, for example for pedagogical reasons, to do so.

## Bibliography*

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.

## Assessment items, weightings and deadlines

Coursework / exam Description Deadline Coursework weighting
Coursework   Test
Exam  Main exam: In-Person, Closed Book, 120 minutes during Summer (Main Period)
Exam  Reassessment Main exam: In-Person, Closed Book, 120 minutes during September (Reassessment Period)

Reassessment strategy:

• If a student fails the test and the exam they will only take the resit exam which will be worth 100%;
• If a student fails the exam but passes the test they will only take the resit exam, the mark for which will be re-aggregated with the test mark;
• If a student fails the test but passes the exam they will take the resit test, the mark for which will be re-aggregated with the exam mark.

### Exam format definitions

• Remote, open book: Your exam will take place remotely via an online learning platform. You may refer to any physical or electronic materials during the exam.
• In-person, open book: Your exam will take place on campus under invigilation. You may refer to any physical materials such as paper study notes or a textbook during the exam. Electronic devices may not be used in the exam.
• In-person, open book (restricted): The exam will take place on campus under invigilation. You may refer only to specific physical materials such as a named textbook during the exam. Permitted materials will be specified by your department. Electronic devices may not be used in the exam.
• In-person, closed book: The exam will take place on campus under invigilation. You may not refer to any physical materials or electronic devices during the exam. There may be times when a paper dictionary, for example, may be permitted in an otherwise closed book exam. Any exceptions will be specified by your department.

Coursework Exam
20% 80%

### Reassessment

Coursework Exam
20% 80%
Module supervisor and teaching staff
Dr Georgi Grahovski, email: gggrah@essex.ac.uk.
Dr Georgi Grahovski
maths@essex.ac.uk

Availability
Yes
Yes
No

## External examiner

Prof Stephen Langdon
Brunel University London
Professor
Resources
Available via Moodle
Of 37 hours, 0 (0%) hours available to students:
0 hours not recorded due to service coverage or fault;
37 hours not recorded due to opt-out by lecturer(s), module, or event type.

Further information

* Please note: due to differing publication schedules, items marked with an asterisk (*) base their information upon the previous academic year.

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.