Module IEA2003:
Mathematical Methods
Module Facts
Run by School of Computer Science and Electronic Engineering
10 Credits or 5 ECTS Credits
Semester 1
Organiser: Dr Daniel Roberts
Overall aims and purpose
To teach the principles of the Fourier Series, Fourier Transform and zTransform, with emphasis on their application in communications engineering and signal processing.
Course content

Revision of trigonometric functions. periodic functions and sinusoids.

Revision of integration by parts: orthogonality of sin(nx), cos(nx). Odd and even functions; halfrange series. Definition of Fourier series and calculation of Fourier coefficients. Infinite sums.

Revision of linear difference equations, and methods of solution of homogeneous and nonhomogeneous equations.

Laurent series and the definition of the ztransform.

Revision of the method of partial fractions, and the solution of linear difference equations using ztransform methods. Shift theorems.

Convolution of sequences and the ztransform of (f * g).

Revision of complex numbers, esp.

exp(jx) = cos(x) + j.sin(x).

In finite integrals. The delta function and the sinc function.

Definition of the Fourier transforms. Transforms of simple functions, properties of the Fourier transform, convolution.
Learning outcomes mapped to assessment criteria
threshold 40% 
good 60% 
excellent 70% 


Understand the principles of Fourier Series. Calculate Fourier coefficients. 
Can sketch simple even, odd and periodic functions. Calculate fundamental angular frequencies and express harmonics as single sinusoids. Knows expressions for Fourier coefficients and can perform simple calculations.  Can also make use of even/odd properties of functions to facilitate calculation. Evaluate functions like x^2.cos(nx) using integration by parts.  Can obtain sums of infinite series by evaluating Fourier series at particular values. Can derive the expressions for the Fourier coefficients. 
Understand the principles of ztransforms. Solve linear difference equations using traditional and ztransform methods. 
Can solve quadratic, homogeneous linear difference equations and find a particular solution to a nonhomogeneous equation. Know the formula for the ztransform. Apply the ztransform to simple functions.  Can solve quadratic, nonhomogeneous, linear difference equations using partial fractions and ztransforms.  Comprehensive knowledge of the ztransform. Can make calculations involving convolution of sequences. 
Understand the principles of Fourier transforms. Calculate simple transforms. 
Know the formula for the Fourier transform. Be familiar with the delta function and the sinc function.  Can correctly apply the Fourier transform to simple functions. Knowledge of the two shift theorems.  Can correctly apply the Fourier transform to complicated functions and take advantage of odd/even properties. 
Assessment Methods
Type  Name  Description  Weight 

Examination  70  
Assignment 1  10  
Assignment 2  10  
Assignment 3  10 
Teaching and Learning Strategy
Hours  

Lecture  2 x 1 Hour lectures over 12 weeks 
24 
Private study  76 
Transferable skills
 Numeracy  Proficiency in using numbers at appropriate levels of accuracy
 SelfManagement  Able to work unsupervised in an efficient, punctual and structured manner. To examine the outcomes of tasks and events, and judge levels of quality and importance
 Critical analysis & Problem Solving  Able to deconstruct and analyse problems or complex situations. To find solutions to problems through analyses and exploration of all possibilities using appropriate methods, rescources and creativity.
Subject specific skills
 Solve problems logically and systematically;
Pre and Corequisite Modules
Corequisite of:
Courses including this module
Compulsory in courses:
 W3H6: BA Music and Electronic Engineering year 2 (BA/MEE)
 H612: BEng Computer Systs Eng (3 yrs) year 2 (BENG/CSE)
 H610: BENG Electronic Engineering (3 yrs) year 2 (BENG/ELE)
 H621: BEng Electronic Engineering with International Experience year 2 (BENG/ELEIE)
 H603: BSc Computer Systems Engineering year 2 (BSC/CSENG)
 H611: BSc Electronic Engineering year 2 (BSC/ELE)
 H661: MEng Control and Instrumentation Engineering year 2 (MENG/CIE)
 H660: MEng Critical Safety Engineering year 2 (MENG/CRSEN)
 H617: MEng Computer Systs Eng (4 yrs) year 2 (MENG/CSE)
 H619: MEng Computer Systems Engineering (with International Exper) year 2 (MENG/CSEIE)
 H601: MEng Electronic Engineering (4 yrs) year 2 (MENG/EE)
 H618: MEng Electronic Engineering with International Experience year 2 (MENG/EEIE)