Module Catalogues, Xi'an Jiaotong-Liverpool University

Module Code: MTH207
Module Title: Vector Fields: Theory and Applications
Module Level: Level 2
Module Credits: 5.00
Semester: SEM1
Originating Department: Mathematical Sciences
Pre-requisites: N/A

 Aims 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.
 Learning outcomes A. Work confidently with different coordinate systems.B. Evaluate line, surface and volume integrals.C. Appreciate the need for the operators div, grad and curl together with the associated theorems of Gauss and Stokes.D. Recognise the many physical situations that involve the use of vector calculus.E. Apply mathematical modelling methodology to formulate and solve simple problems in electromagnetism and inviscid fluid flow.
 Method of teaching and learning This module will be delivered by a combination of formal lectures and tutorials.
 Syllabus Different coordinate systems. Scalar and vector fields; electrostatic field, Lagrangian and Eulerian descriptions of a fluid. Gradient; E = -grad f , 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.
Delivery Hours
 Lectures Seminars Tutorials Lab/Prcaticals Fieldwork / Placement Other(Private study) Total Hours/Semester 39 13 98 150

## Assessment

 Sequence Method % of Final Mark 1 Mid-Term 15.00 3 Final Exam 85.00
 Module Catalogue generated from SITS CUT-OFF: 1/26/2020 10:55:40 PM