This course covers techniques for evaluating integrals in two and three dimensions, line integrals in space and the use of Green's theorem, provides an introduction to vector calculus and vector fields, and the application of integral theorems to the evaluation of surface integrals.

2 lecture hours per week
5 hours tutorials

None

None

85% Examination

15% Moodle Quiz

The aims of this course are to:

■ revise and extend of Double Integration techniques

■ introduce techniques for evaluating line integrals in space, and the use of Green's theorem

■ provide an introduction to vector calculus and vector fields, with particular interest in conservative and irrotational vector fields

■ application of the integral theorems to calculating surface integrals.

By the end of this course students will be able to:

■ evaluate line integrals in 2 and 3 dimensions;

■ evaluate line integrals using Green's Theorem;

■ find a (unit) normal vector to a surface;

■ calculate the gradient of a scalar function;

■ calculate directional derivatives and find their maximum value;

■ state what a conservative vector field is, what a potential function is, and be able to calculate a potential function for a conservative vector field;

■ state when a vector field is solenoidal;

■ state Laplace's equation and define a harmonic function;

■ calculate the curl of a vector field;

■ solve simple identities involving gradient, divergence and curl;

■ state what an irrotational vector field is and the relationship between conservative and irrotational vector fields;

■ evaluate surface integrals using Gauss' Divergence Theorem.

Students must attend the degree examination and submit at least 75% by weight of the other components of the course's summative assessment.

Students should attend at least 75% of the timetabled classes of the course.

Note that these are minimum requirements: good students will achieve far higher participation/submission rates.  Any student who misses an assessment or a significant number of classes because of illness or other good cause should report this by completing a MyCampus absence report.