MA210-5-AU-CO:
Vector Calculus
2024/25
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Autumn
Undergraduate: Level 5
Current
Thursday 03 October 2024
Friday 13 December 2024
15
04 January 2024
Requisites for this module
(none)
(none)
(none)
(none)
MA222, MA225, MA323
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
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.
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.
By the end of the module, students will be expected to:
- 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.
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.
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.
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Adams, R.A., Essex, C. and Norges teknisk-naturvitenskapelige universitet (2020a)
Calculus: a complete course. Ninth edition. Edited by M.A. Nome. Harlow, England: Pearson. Available at:
https://app.kortext.com/Shibboleth.sso/Login?entityID=https://idp0.essex.ac.uk/shibboleth&target=https://app.kortext.com/borrow/615754.
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Adams, R.A., Essex, C. and Norges teknisk-naturvitenskapelige universitet (2020b)
Calculus: a complete course. Ninth edition. Edited by M.A. Nome. Harlow, England: Pearson. Available at:
https://app.kortext.com/Shibboleth.sso/Login?entityID=https://idp0.essex.ac.uk/shibboleth&target=https://app.kortext.com/borrow/615755.
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Lipschutz, S., Spiegel, M.R. and Spellman, D. (2009)
Schaum's outline: Vector analysis. Second edition. New York: McGraw-Hill. Available at:
https://ebookcentral.proquest.com/lib/universityofessex-ebooks/detail.action?docID=6404211.
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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 |
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)
|
Additional coursework information
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.
Your department will provide further guidance before your exams.
Overall assessment
Reassessment
Module supervisor and teaching staff
Dr Georgi Grahovski, email: gggrah@essex.ac.uk.
Dr Georgi Grahovski
maths@essex.ac.uk
Yes
Yes
No
Prof Stephen Langdon
Brunel University London
Professor
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.
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