Provide an understanding of the various vector integrals, the operators div, grad and curl and the relations between them.

Develop an appreciation of the many applications of vector calculus to physical situations.

Provide an introduction to the subjects of fluid mechanics and electromagnetism.

(LO1) Work confidently with different coordinate systems.

(LO2) Know how to evaluate line, surface and volume integrals.

(LO3) Understand how the operators div, grad and curl together with the associated theorems of Gauss and Stokes are used.

(LO4) Recognise the many physical situations that involve the use of vector calculus.

(LO5) Apply mathematical modelling methodology to formulate and solve simple problems in electromagnetism and inviscid fluid flow.

Different coordinate systems.

Scalar and vector fields; electrostatic field, Lagrangian and Eulerian descriptions of a fluid.

Gradient; E = -grad Ф , dipole field, convective derivative D/Dt.

Surface and volume integrals; divergence, Gauss' theorem, equation of continuity, incompressible flows.

Curl, line integrals, Stokes' theorem; irrotational fields, conservative fields, velocity potential.

Maxwell's equations, wave equation, acceleration of a fluid particle.

Applications to fluid motion; inviscid fluids, boundary conditions, pressure, Euler equation and solutions for irrotational motion and steady motion.