Vector Calculus

Summary module description:
The first part of 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 second part of the module involves line, surface and volume integrals. In the third part various relationships between differential operators and integration (e.g, Green's, 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:
? understand and apply the concepts of vector calculus
? derive differential identities and integral theorems of vector calculus

Additional outcomes:
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:
First part: 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, irrotational and conservative fields, scalar and vector potentials. Total derivatives and chain rule for fields.

Second part: 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.

Third part: Green?s, divergence and Stokes? theorems and their applications.
Brief description of teaching and learning methods:
Lectures supported by problem sheets and lecture-based tutorials.

Summative Assessment Methods:
Written exam 80%
Set exercise 20%

Other information on summative assessment:
Two assignments and one examination paper.

Formative assessment methods:
Problem sheets.

Penalties for late submission:
The Module Convener will apply the following penalties for work submitted late, in accordance with the University policy.
where the piece of work is submitted up to one calendar week after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for the piece of work will be deducted from the mark for each working day (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.

Length of examination:
2 hours.

Requirements for a pass:
A mark of 40% overall.