Module Title:   Partial Differential Equations

Module Credit:   20

Module Code:   CM-0344D

Academic Year:   2015/6

Teaching Period:   Semester 1

Module Occurrence:   A

Module Level:   FHEQ Level 6

Module Type:   Standard module

Provider:   Computer Science

Related Department/Subject Area:   School of Electrical Engineering & Computer Science

Principal Co-ordinator:   Dr Ci Lei

Additional Tutor(s):   -

Prerequisite(s):   CM-0225D

Corequisite(s):   None

Aims:
To extend the knowledge of the solution of ordinary differential equations to partial differential equations (PDEs).

Learning Teaching & Assessment Strategy:
The basic theory and illustrative examples are presented and developed in formal lectures. Complementary tailor-made example sheets are provided. These are discussed, and assistance with their solution is provided in tutorials, either on a one-to-one basis or as a staff or student-led group, as appropriate.

Formative exercises encourage the ongoing digestion of the material, with the extent of the cumulative knowledge and skills acquired assessed through a coursework assignment and a formal examination.

Lectures:   12.00          Directed Study:   150.00           
Seminars/Tutorials:   24.00          Other:   0.00           
Laboratory/Practical:   12.00          Formal Exams:   2.00          Total:   200.00

On successful completion of this module you will be able to...

show a breadth of knowledge of the solution of PDEs.

On successful completion of this module you will be able to...

manipulate with and apply the fundamental principles of solution of physically-occurring realistic PDEs.

On successful completion of this module you will be able to...

learn and work independently with patience and persistence using good general skills of organization and time-management, be adaptable with a highly-developed ability to assess problems from new areas logically through an analytical approach, write coherently and clearly communicate results.

  Coursework   30%
 
  Individual Coursework
  Examination - closed book 2.00 70%
 
  Examination
  Examination - closed book 3.00 100%
 
  Supplementary examination

Outline Syllabus:
INTRODUCTORY THEORY: nomenclature for PDEs and some important equations; 1st order PDEs: particle kinetic equation, method of characteristics. 2nd order PDEs: classification and reduction, classification of boundary conditions. WAVE EQUATIONS: D`Alembert`s solution, steady-state and transient heat equation. SEPARATION OF VARIABLES: simple 1-D and 2-D cases, Fourier series, heat conductivity in rod. Laplace`s equation in 2-D polar coordinates, and in cylindrical coordinates. GREEN`S FUNCTION: inverse differential operator as an integral operator. General 1-D Sturm-Liouville boundary value problems: Lagrange identity and boundary value problem; orthonormal functions and the Kronecker delta-function; homogeneous, non-homogeneous and singular Sturm-Liouville problems.

Version No:  4