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) Derive and analyse equations of surfaces/curves in Cartesian, cylindrical and spherical systems of coordinates.

(LO2) Analyse and evaluate line, surface and volume integrals, including evaluation in curvilinear coordinates.

(LO3) Use the operators div, grad and curl together with the associated theorems of Gauss and Stokes, and evaluation of line, surface and volume integrals.

(LO4) Solve routine problems involving mathematical models for physical problems using vector calculus.

(LO5) Derive governing equations of the fluid flow. Analyse and solve model problems occurring in inviscid fluid flow.

(LO6) Analyse and formulate mathematical models for physical problems, related to fluid flow, that involve the use of vector calculus.

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.