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 Professor AE Faraggi
Mathematical Sciences
Alon.Faraggi@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) 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
Final Assessment (open book and remote) One hour time on task There is a resit opportunity. Standard UoL penalty applies for late submission. Assessment Schedule (When) :First Semester  one hour time on tas    50       
CONTINUOUS Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
Homework 1 Equivalent to 2-5 sides of A4  Equivalent to 2-5 si    10       
Class Test (open book and remote) Around 60-90 minutes Non-standard penalty applies for late submission - Assessment Schedule (When) :First Semester  Around 60-90 minutes    20       
Homework 2 Equivalent to 2-5 sides of A4  Equivalent to 2-5 si    10       
Homework 3 Equivalent to 2-5 sides of A4  Equivalent to 2-5 si    10