Module Content

Vectors and Scalars: Lines and planes in three-dimensional space, Parametric representations of curves and surfaces, Vector and scalar fields, Polar coordinate systems. 

Vector Differentiation: Ordinary and partial derivatives; Space curves; Applications. 

Differential Geometry: Regular space curves and the Frenet-Serret formulae. 

Vector Differential Operators: Div, grad and curl, and their applications. 

Vector Integration: Line, surface and volume integrals; Conservative fields. 

Vector Integration Theorems (with Proofs): Green’s theorem, Divergence theorem, Stokes’s theorem. 

Curvilinear Coordinates: Definitions; Div, grad and curl in general and specific orthogonal curvilinear coordinates.

Teaching Methods

The module will be delivered on campus, with weekly lecture and tutorial sessions. 

Printed notes will be given ahead of time for each section of the course, to support and enhance students’ preparation and engagement during class sessions. Lectures will follow the notes, with discussions of the main theoretical topics, and study of examples of the applications of the theory. There will be a strong emphasis on student involvement in discussions in lectures, to encourage a more active approach to learning the material, and to allow the delivery to be tailored to build on the students’ current understanding. 

Regular formative work in tutorial sessions will allow students to internalise the mathematical ideas and methods developed in the lectures, and lead to the development of problem-solving skills. This formative work will also feed back into the delivery of lectures and tutorials. 

Assessment Methods

The module is assessed through a portfolio of exercises and an examination.