### Module Details

 The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module.
 Title FIELD THEORY AND PARTIAL DIFFERENTIAL EQUATIONS Code MATH283 Coordinator Professor DI Jack Mathematical Sciences Dij@liverpool.ac.uk Year CATS Level Semester CATS Value Session 2021-22 Level 5 FHEQ First Semester 7.5

### Aims

To introduce students to the concepts of scalar and vector fields. To develop techniques for evaluating line, surface and volume integrals. To introduce students to some of the basic methods for solving partial differential equations

### Learning Outcomes

(LO1) After completing the module, students should be able to: Evaluate Grad, Div, Curl and Laplacian operators in Cartesian and polar coordinates Evaluate line, double and volume integrals Have a good understanding of the physical meaning of flux and circulation  Be able to solve simple boundary value problems for the wave equation, diffusion equation and Laplace's equation

### Syllabus

Vector Calculus:  Revision of partial differentiation; scalar and vector fields; field operators Grad, Div, Curl, and the Laplacian; Line, double, surface and volume integrals (spheres and cuboids only); flux and circulation of vector field, theorems of Gauss and Stokes; potential functions; applications to electromagnetism. Partial Differential Equations:  Basic equations of mathematical physics, wave equation, diffusion equation, Laplace's equation; solution by method of separation of variables; calculation of eigenfunctions for simple initial and boundary value problems.

### Assessment

EXAM Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
Final Assessment (open book and remote) one hour time on task There is a resit opportunity. Standard UoL penalty applies for late submission.  one hour time on tas    50
CONTINUOUS Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
Class Test (open book and remote) around 60-90 minutes Standard UoL penalty applies for late submission. Assessment Schedule (When) :First semester  around 60-90 minutes    20
Homework 10%  Equivalent to 2-5 si    10
Homework  Equivalent to 2-5 si    10
Homework  Equivalent to 2-5 si    10