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 Prof SM Rees
Mathematical Sciences
Maryrees@liverpool.ac.uk
Year CATS Level Semester CATS Value
Session 2016-17 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

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
1 

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.


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

Pre-requisites before taking this module (other modules and/or general educational/academic requirements):
This module is for non-XJTLU students 

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:H646 Year:2 Programme:H670 Year:2 Programme:H602 Year:2 Programme:H606 Year:2 Programme:H603 Year:2 Programme:H604 Year:2 Programme:H610 Year:2 Programme:H612 Year:2 Programme:H620 Year:2 Programme:H621 Year:2 Programme:H645 Year:2 Programme:H651 Year:2

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
Unseen Written Exam  2 hours  First semester  80  Yes  Standard UoL penalty applies  Assessment 2 Notes (applying to all assessments) Assessment 1: Class test (10%) and marked homework (10%). Assessment 2: Exam rubric: Attempt FOUR questions only. All questions are of equal value (25 marks each).  
CONTINUOUS Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
Coursework  Homeworks, and Class  First semester  20  No reassessment opportunity  Standard UoL penalty applies  Assessment 1 There is no reassessment opportunity,