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COMO301 Mathematical Modelling 1

Second Semester, 18 points

Not available in 2011

Mathematical modeling is the link between mathematics and the rest of the world. You are presented with a question. You think a bit, and then you refine the question, phrasing it in precise mathematical terms. Once the question becomes a mathematics question, you use mathematics to find an answer. If the problem is messy (and real problems usually are) then you use appropriate computer techniques to handle the messy details. Then you have to reverse the process, translating the mathematical solution back into plain English. In COMO 301 you will learn to formulate mathematical models for real-world problems, solve those problems using modern mathematical and computer techniques, and express your conclusions in a way that normal, intelligent people can understand, even if they never took Calculus. In particular, control theory studies systems that we want to control; for has a growing list of important applications see the side-bar.

Paper details

Students in COMO 301 will learn that advanced mathematical and computer techniques are not only relevant but necessary to solve real problems. We will learn about control theory, nonlinear optimization, dynamical systems, and random processes in a natural and intuitive way, in the context of real problems from science, engineering, commerce, medicine, and agriculture. We will learn to use modern computational tools including graphics, spreadsheets, computer algebra systems (Mathematica), and commercial software packages (Matlab).

Main topics

The main module will be on control theory. Systems evolve according to laws given by differential equations. We can influence the behaviour of a system by varying a given set of controls, for example the accelerator of a car, or the rate of investment, or the power fed to an oven. The performance of the system is measured by an objective function, for instance the time taken or the fuel used . The task is to find the control that gives the best results. The course starts with the technique of dynamic programming to solve simple discrete problems. You will solve systems of differential equations as covered in MATH 262 , Mathematical Methods, which will be reviewed as required. You will also use computer software to solve and to visualize control systems.

Other modules will cover topics such as dynamical systems and chaos, modelling of solids and elasticity, stochastic modelling.

Prerequisites

COMO 101 and MATH 251. MATH 242 and MATH 262 are recommended.

Lecturers

Dr. Gerrard Liddell

Lectures

Mondays and Wednesdays at 10.00 in Room 241 (Laboratory B) Science III Bldg.

Teaching methods

Each week consists of two lectures, a tutorials (10.00-11.00 Friday) and laboratory time (15.00-17.00 Tuesday).

Internal assessment

Internal assessment will consist of regular exercises, mini-projects, presentations and a test on each module.

Final mark

The final mark F is calculated from:
F = A
where A (internal assessment) is out of 100.


Plagiarism

Students should make sure that all submitted work is their own. “Plagiarism is a form of dishonest practice. Plagiarism is defined as copying or paraphrasing another’s work and presenting it as one’s own” (University of Otago Calendar). In practice this means that plagiarism includes any attempt in any piece of submitted work (e.g. an assignment or test) to present as one’s own work the work of another (whether of another student or a published authority). Any student found to be responsible for plagiarism in any piece of work submitted for assessment shall be subject to the University’s dishonest practice regulations which may result in various penalties, including forfeiture of marks for the piece of work submitted, a zero grade for the paper, or in extreme cases exclusion from the University. The University of Otago reserves the right to use plagiarism detection tools.

While we strive to keep details as accurate and up-to-date as possible, information given here should be regarded as provisional. Individual lecturers will confirm teaching and assessment methods.