To provide an understanding of the various vector integrals, the operators div, grad and curl and the relations between them. To give an appreciation of the many applications of vector calculus to physical situations. To provide an introduction to the subjects of fluid mechanics and electromagnetism.

(LO1) After completing the module students should be able to: - Work confidently with different coordinate systems. - Evaluate line, surface and volume integrals. - Appreciate the need for the operators div, grad and curl together with the associated theorems of Gauss and Stokes. - Recognise the many physical situations that involve the use of vector calculus. - Apply mathematical modelling methodology to formulate and solve simple problems in electromagnetism and inviscid fluid flow. All learning outcomes are assessed by both examination and course work.

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.