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

100% In person Examination

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.