Module Title:   Mathematical Methods

Module Credit:   20

Module Code:   CM-0227D

Academic Year:   2015/6

Teaching Period:   Semester 2

Module Occurrence:   A

Module Level:   FHEQ Level 5

Module Type:   Standard module

Provider:   Computer Science

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

Principal Co-ordinator:   Professor A Vourdas

Additional Tutor(s):   -

Prerequisite(s):   CM-0125L     ENG1074L

Corequisite(s):   None

Aims:
To review the calculus of functions of two variables. To present an introduction to the theory of Fourier series and vector calculus.

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.The module is assessed in its entirety by a formal examination. Supplementary assessment is as original.

Lectures:   36.00          Directed Study:   161.50           
Seminars/Tutorials:   0.00          Other:   0.00           
Laboratory/Practical:   0.00          Formal Exams:   2.50          Total:   200.00

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

show a breadth of knowledge of the techniques of two-variable calculus, Fourier series and vector calculus.

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

manipulate with and apply in simple cases the fundamental theory of two-variable calculus, Fourier series and vector calculus.

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 readiness to assess problems from new areas logically through an analytical approach, write coherently and clearly communicate results.

  Examination - closed book 2.50 100%
 
  Closed Book Examination (two and a half hours)

Outline Syllabus:
FUNCTIONS OF TWO VARIABLES: partial differentiation; stationary points in two variables; Taylor`s theorem in two variables. FOURIER SERIES: orthogonality of sines and cosines; odd and even functions; calculus of Fourier series; Parseval`s theorem.VECTOR CALCULUS: scalar and vector fields; vector operators; gradient; directional derivative; divergence; curl; Laplacian; identities. LINE INTEGRALS: curves, properties and evaluation of line integrals. TRIPLE INTEGRALS. SURFACE INTEGRALS: evaluation; curvilinear coordinates; surface area; unit normal and orientation of surfaces. INTEGRAL THEOREMS. Gauss divergence theorem.

Version No:  2