MA2VCNU-Vector Calculus

Module Provider: Mathematics and Statistics
Number of credits: 10 [5 ECTS credits]
Terms in which taught: Spring term module
Pre-requisites: MA0MANU Mathematical Analysis and MA1DE1NU Differential Equations I and MA1LANU Linear Algebra
Non-modular pre-requisites:
Modules excluded:
Current from: 2020/1

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 place, the divergence and Stokes’ theorems) are derived and demonstrated.

The Module lead at NUIST is Dr. Vahid Darvish


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

Assessable learning outcomes:

By the end of the course, students are expected to be able:

  • Demonstrate problem solving skills;

  • Understand and apply the concepts of vector calculus;

  • Derive and apply differential identities and integral theorems of vector calculus.

Additional outcomes:

Students will develop a thorough knowledge of mathematical notation, and an improved ability to interpret mathematical expressions. They will be able to manipulate different mathematical objects, such as 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, irrotational 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 enhanced by self-study and peer-group learning.

Contact hours:
  Autumn Spring Summer
Lectures 45
Guided independent study: 55
Total hours by term 0 100 0
Total hours for module 100

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

Summative assessment- Examinations:

2 hours.

Summative assessment- Coursework and in-class tests:

One examination and a number of assignments.

Formative assessment methods:

Problem sheets.

Penalties for late submission:

The Module Convenor 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:
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).

Additional Costs (specified where applicable):

Last updated: 17 September 2020


Things to do now