# Module IEA-2004:Eng Analysis: Linear Systems

### Module Facts

Run by School of Computer Science and Electronic Engineering

10 Credits or 5 ECTS Credits

Semester 2

Organiser: Dr Iestyn Pierce

### Overall aims and purpose

To teach the principles of the Laplace Transform and its application in the study of differential equations and linear systems. Particular attention will be given to forced second order systems, resonance and applications in network analysis. Graphical methods for qualitative examination of ODEs will be introduced.

### Course content

• Second order ODEs, forced systems, graphical methods for visualizing solutions, phase portraits. • Resonance in electrical and mechanical systems, general form for a second order system. • Definition of the Laplace transforms. Basic signals, shift theorems, convolution. • Ordinary Differential Equations, Transfer functions, Complex Impedance. • Applications of the Laplace transform in control systems and network synthesis • Cauer Ladders, Active Filters. • Relationship with the Fourier transform, Steady State Sinusoidal response

### Learning outcomes mapped to assessment criteria

threshold

40%

good

60%

excellent

70%

Understand the principles and properties of forced second order systems and methods for their graphical solution.

Can state definitions and basic properties of 2nd order systems. Can describe what is meant by damping factor/Q-factor and natural frequency. Can use standard solution techniques. Can discuss graphical methods at a reasonable level. Demonstrates thorough knowledge of second order systems in general, including graphical methods.

Understand the Laplace transform and its engineering applications.

Know the formula for the Laplace transform. Can state basic results. Apply the Laplace transform to solution of ODEs. Knows and can apply all the standard results. A comprehensive knowledge of Laplace transform methods. Evaluates results and derivations sensibly.

### Assessment Methods

Type Name Description Weight
Examination 80
Application of graphical methods 20

### Teaching and Learning Strategy

Hours
Lecture

2 x 1 hour Lectures per week for 12 weeks (4 x 1 hour tutorials delivered over 12 weeks during lecture slots).

24
Private study

Worked examples, attempting tutorial questions, completing past exam papers, revision.

76

### Transferable skills

• Literacy - Proficiency in reading and writing through a variety of media
• Numeracy - Proficiency in using numbers at appropriate levels of accuracy
• Computer Literacy - Proficiency in using a varied range of computer software
• Self-Management - 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
• Exploring - Able to investigate, research and consider alternatives
• 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.
• Presentation - Able to clearly present information and explanations to an audience. Through the written or oral mode of communication accurately and concisely.

### Subject specific skills

• Apply underpinning concepts and ideas of engineering;
• Solve problems logically and systematically;