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, Partial Differential Equations & Methods of Solution
Code MATH282
Coordinator Dr PEL Rakow
Mathematical Sciences
Rakow@liverpool.ac.uk
Year CATS Level Semester CATS Value
Session 2019-20 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) Evaluate Grad, Div, Curl and Laplacian operators in Cartesian and polar coordinates

(LO2) Evaluate line, double and volume integrals

(LO3) Have a good understanding of the physical meaning of flux and circulation

(LO4) Be able to solve boundary value problems for partial differential equations

Syllabus
 

Review of vector calculus: Grad, Div, Curl, Gauss’ theorem, Stokes’ theorem.  Maxwell’s equations: in the language of vector calculus, as well as ODEs and PDEs. Advanced applications including derivation of physical laws. Laplace and Fourier transforms to solve ODEs, Fourier series to solve PDEs, central difference numerical integration methods to solve ODEs and PDEs.

Recommended Texts
Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module.

Pre-requisites before taking this module (other modules and/or general educational/academic requirements):
 

Co-requisite modules:
 

Modules for which this module is a pre-requisite:
 

Programme(s) (including Year of Study) to which this module is available on a required basis:
 

Programme(s) (including Year of Study) to which this module is available on an optional basis:
 

Assessment
EXAM Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
Assessment 2 Standard UoL penalty applies for late submission. Assessment Schedule (When) :First Semester  2 hours    80       
CONTINUOUS Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
Assessment 1 Non-standard penalty applies for late submission - Assessment Schedule (When) :First Semester  Class Test, Homework    20