Module IBC-2003:
Engineering analysis 1
Engineering analysis I: mathematical methods 2023-24
IBC-2003
2023-24
School of Computer Science & Engineering
Module - Semester 1
10 credits
Module Organiser:
Iestyn Pierce
Overview
• Revision of trigonometric functions. periodic functions and sinusoids. • Revision of integration by parts: orthogonality of sin(nx), cos(nx). Odd and even functions; half-range series. Definition of Fourier series and calculation of Fourier coefficients. Infinite sums. • Gram-Schmidt algorithm, Function spaces as vector spaces • Revision of linear difference equations, and methods of solution of homogeneous and non-homogeneous equations. • Laurent series and the definition of the z-transform. • Revision of the method of partial fractions, and the solution of linear difference equations using z-transform methods. Shift theorems. • Convolution of sequences and the z-transform 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.
• Revision of trigonometric functions. periodic functions and sinusoids.
• Revision of integration by parts: orthogonality of sin(nx), cos(nx). Odd and even functions; half-range series. Definition of Fourier series and calculation of Fourier coefficients. Infinite sums.
• Gram-Schmidt algorithm, Function spaces as vector spaces
• Revision of linear difference equations, and methods of solution of homogeneous and non-homogeneous equations.
• Laurent series and the definition of the z-transform.
• Revision of the method of partial fractions, and the solution of linear difference equations using z-transform methods. Shift theorems.
• Convolution of sequences and the z-transform 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.
Assessment Strategy
-threshold -Equivalent to 40%. Uses key areas of theory or knowledge to meet the Learning Outcomes of the module. Is able to formulate an appropriate solution to accurately solve tasks and questions. Can identify individual aspects, but lacks an awareness of links between them and the wider contexts. Outputs can be understood, but lack structure and/or coherence.
-good -Equivalent to the range 60%-69%. Is able to analyse a task or problem to decide which aspects of theory and knowledge to apply. Solutions are of a workable quality, demonstrating understanding of underlying principles. Major themes can be linked appropriately but may not be able to extend this to individual aspects. Outputs are readily understood, with an appropriate structure but may lack sophistication.
-excellent -Equivalent to the range 70%+. Assemble critically evaluated, relevant areas of knowledge and theory to construct professional-level solutions to tasks and questions presented. Is able to cross-link themes and aspects to draw considered conclusions. Presents outputs in a cohesive, accurate, and efficient manner.
Learning Outcomes
- Understand the principles of Fourier Series.
Calculate Fourier coefficients.
- Understand the principles of Fourier transforms.
Calculate simple transforms.
- Understand the principles of z-transforms. Solve linear difference equations using z-transform methods.
Assessment method
Exam (Centrally Scheduled)
Assessment type
Summative
Description
Unseen examination
Weighting
70%
Assessment method
Coursework
Assessment type
Summative
Description
Assignment 1
Weighting
10%
Assessment method
Coursework
Assessment type
Summative
Description
Assignment 2
Weighting
10%
Assessment method
Coursework
Assessment type
Summative
Description
Assignment 3
Weighting
10%