MA210-5-AU-CO:
Vector Calculus
2020/21
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Autumn
Undergraduate: Level 5
Future
Thursday 08 October 2020
Friday 18 December 2020
15
28 May 2020
Requisites for this module
(none)
(none)
(none)
(none)
MA225, MA323
MSCIG199 Mathematics and Data Science
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.
To introduce the classical theory of vector calculus, including vector differential operators and line and surface integrals, and associated applications.
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.
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.
This module consists of 30 contact hours consisting of 25 lectures and five classes. There are three revision lectures in the summer term.
This module does not appear to have a published bibliography.
Assessment items, weightings and deadlines
| Coursework / exam |
Description |
Deadline |
Coursework weighting |
| Coursework |
Test 1 |
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| Coursework |
Test 2 |
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| Exam |
Main exam: 120 minutes during Summer (Main Period)
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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.
Your department will provide further guidance before your exams.
Overall assessment
Reassessment
Module supervisor and teaching staff
Prof Edward Codling, email: ecodling@essex.ac.uk.
Prof Edward Codling, email ecodling@essex.ac.uk
Professor Edward Codling (ecodling@essex.ac.uk)
Yes
Yes
No
Dr Tania Clare Dunning
The University of Kent
Reader in Applied Mathematics
Prof Stephen Langdon
Brunel University London
Professor
Available via Moodle
Of 37 hours, 33 (89.2%) hours available to students:
4 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).
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