Purpose of the assessment:

The purpose of this assignment is to investigate practical applications of complex mathematical concepts and gain understanding of how mathematics is used in engineering context. This assignment provides an opportunity for the students to enhance problem solving skills as well the familiarity in using MATLAB as a problem solving tools.

Description of the assessment:

This task requires you to research and try to understand the given topic, methods and how MATLAB is used as a problem solving tool in the given document.

Modern mathematics requires the use of computational tools in order to solve difficult real world problems. Tools are required because often the problems are either too large or not possible to solve analytically, and building physical models is impractical. Using computational tools is additionally often an open ended exercise, where some formal theory is implemented, possibly with the aid of pre-existing analysis or models. This assignment gives you a chance to investigate into application of complex mathematical concepts and gain hands on experience in how MATLAB is used as a problem solving tool. The Engineering Mathematics Course unit assists you to become familiar with the mathematical skills required to solve engineering related problems. The mathematical skills acquired in this Engineering Mathematics Course unit will provide necessary background to understand the algorithms and methods used in these documents.

You need to

- Show how well you have understood the topic and
- Algorithms or the method described in the document
- Show how well you have understood simulations or calculations in this system and explain how MATLAB is used as a problem solving tool
- Finally develop simulations that can be readily tested in MATLAB, that provide a feel for the topic of choice.

Topics
- Solve a System of Differential Equations
- Modelling Sound in MATLAB
- Graphical Approach to Solving Inequalities
- Curve fitting and Polynomial interpolation.
- Solving ODEs in MATLAB
- Predator-Prey Equations
- Tracking Pedestrians from a Moving Car.

1. Select a topic from the above list, research the topic and try to understand the topic, method and underlying equations governing the system which in general will not be easy to solve analytically.

2. Research existing simulations or calculations in this system, and develop simulations that can be readily tested in MATLAB, that provide a feel for the topic of choice.

3. Prepare a report summarizing your findings. Your report should include the following:
a. The cover page must identify student (name and number), teaching staff, and assignment.
b. The assignment must use 12 point font size minimum and at least single line spacing with appropriate section headings.
c. Body of the report should include

i. Introduction -In this section, you need to give a brief overview and your understanding of the problem discussed in the document. And outline of the report ( in 3-4 sentences)

ii. Analyse -You need to describe your understanding of methods and algorithms described in the selected topic, with your own words.

iii. Design - You need to describe your understanding of simulations or calculations in this system and how you develop simulations that can be readily tested in MATLAB, that provide a feel for the topic of choice. Example:

1. Is your implementation exactly the same as the algorithm described in the paper? If they are not exactly the same, why did you make those changes?

a. (The reason might be: (1) you think they can lead to better performance; (2) one component of the original algorithm is very complicated and difficult to implement, so that you used a simpler approach;(3) any other reasons.))

2. You do not have to make your approach different from that in the original paper - if you can implement the original algorithm exactly and perfectly, you have done a wonderful job.

3. Include your Code- Briefly explain the key files and functions in your code, (do not include if it is longer than 3 pages-then you can attach the code to Appendix)

iv. Results and conclusion - Present quantitative and qualitative results of your approach and conclusion. Illustrative results please pick some images and show your results on them.

v. Reference sources must be cited in the text of the report, and listed appropriately at the end in a reference list.

4. Prepare a PowerPoint presentation for 5-10 minute presentation. No more than 7-8 slides. You must present as a group, every member of your group needs to speak. You must have visual aids to support your presentation and you must acknowledge the source of the information you present. The presentation should focus on the Mathematics and demonstrate some of the discoveries and their application.

5. The assignment must be submitted in soft (electronic) copy under Moodle as well as submitted in hard (printed) copy to the level 6 assignment centre. The MATLAB program file and presentation should also be uploaded. The pages of the assignment must be clear on each page.