MA3VC-Vector Calculus

Module Provider: Mathematics and Statistics
Number of credits: 10 [5 ECTS credits]
Level:6
Terms in which taught: Autumn term module
Pre-requisites: MA1CA Calculus and MA1LA Linear Algebra
Non-modular pre-requisites:
Co-requisites:
Modules excluded: MA2VC Vector Calculus
Current from: 2018/9

Module Convenor: Dr Peter Chamberlain

Type of module:

Summary module description:

The module involves differentiation of scalar and vector fields by the gradient, Laplacian, divergence and curl differential operators. A number of identities for the differential operators are derived and demonstrated. The module also involves line, surface and volume integrals. Various relationships between differential operators and integration (e.g, Green's theorem in the plane, the divergence and Stoke's theorems) are derived and demonstrated.

Aims:
To introduce and develop the ideas and methods of vector calculus.

Assessable learning outcomes:

By the end of the module students are expected to be able to:

• demonstrate problem solving skills;

• understand the concepts of vector calculus;

• derive and apply differential identities and integral theorems of vector calculus;

• describe, apply and otherwise use methods and concepts beyond those covered in lectures.

Students will develop a more thorough knowledge of mathematical notation and an improved ability to interpret mathematical expressions and to manipulate different mathematical objects (e.g. scalar and vector quantities).

Outline content:

Vector fields and vector differential operators. Scalar fields, vector fields, vector functions (curves). Vector differential operators: partial derivatives, gradient, Jacobian matrix, Laplacian, divergence, curl. Vector differential identities. Solenoidal, irrational and conservative fields, scalar and vector potentials.

Vector integration. Line integrals of scalar and vector fields. Independence of path, line integrals for conservative fields and fundamental theorem of vector calculus. Double and triple integrals, change of variables. Surface integrals, unit normal fields, orientations and flux integrals. Special coordinate systems: polar, cylindrical and spherical coordinates.

Green’s theorem in the plane, divergence and Stokes’ theorems and their applications.

Brief description of teaching and learning methods:
Lectures supported by problem sheets and lecture-based tutorials

Contact hours:
 Autumn Spring Summer Lectures 20 Tutorials 10 Guided independent study 70 Total hours by term 100.00 Total hours for module 100.00

Summative Assessment Methods:
 Method Percentage Written exam 70 Set exercise 30

Summative assessment- Examinations:
2 hours.

Summative assessment- Coursework and in-class tests:

Assignments and one examination paper (level 6).

Formative assessment methods:
Problem sheets.

Penalties for late submission:
The Module Convener will apply the following penalties for work submitted late:

• where the piece of work is submitted after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for that piece of work will be deducted from the mark for each working day[1] (or part thereof) following the deadline up to a total of five working days;
• where the piece of work is submitted more than five working days after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.

• The University policy statement on penalties for late submission can be found at: http://www.reading.ac.uk/web/FILES/qualitysupport/penaltiesforlatesubmission.pdf
You are strongly advised to ensure that coursework is submitted by the relevant deadline. You should note that it is advisable to submit work in an unfinished state rather than to fail to submit any work.

Assessment requirements for a pass:
A mark of 40% overall.

Reassessment arrangements:
One examination paper of 2 hours duration in August/September - the resit module mark will be the higher of the exam mark (100% exam) and the exam mark plus previous coursework marks (70% exam, 30% coursework).