Mathematical Methods
20
CM0227D
2015/6
Semester 2
A
FHEQ Level 5
Standard module
Computer Science
School of Electrical Engineering & Computer Science
Professor A Vourdas

CM0125L ENG1074L
None
To review the calculus of functions of two variables. To present an introduction to the theory of Fourier series and vector calculus.
The basic theory and illustrative examples are presented and developed in formal lectures. Complementary tailormade example sheets are provided. These are discussed, and assistance with their solution is provided in tutorials, either on a onetoone basis or as a staff or studentled group, as appropriate.The module is assessed in its entirety by a formal examination. Supplementary assessment is as original.
Study Hours:  
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 twovariable 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 twovariable 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 timemanagement, be adaptable with a readiness to assess problems from new areas logically through an analytical approach, write coherently and clearly communicate results.
001.  Assessment Type  Duration  Percentage 
Examination  closed book  2.50  100%  
Description  
Closed Book Examination (two and a half hours) 
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.
2