Information on this page, including unit offerings, is from the 2019 academic year.
Mathematical Modelling (MAS221)
|Organisational Unit||Information Technology, Mathematics and Statistics|
|Availability||MURDOCH: S2-internal, S2-external|
|Teaching Timetables||Murdoch S2
|Description||This unit considers mathematical models, their uses and limitations. Case studies involving relatively simple mathematical ideas will demonstrate that models range from simple tools for answering 'what if' questions to quite accurate descriptions that allow useful predictions to be made. Topics include the: modelling of chemical, biological and physical systems (using first order ordinary differential equations); modelling of steady state systems (using matrix algebra); dynamical models (using ordinary differential equations); and modelling of diffusive processes (using partial differential equations).|
|Unit Learning Outcomes||On successful completion of the unit you should be able to:
1. Construct and understand basic mathematical models of simple biological, environmental and other systems.
2. Carry out mathematical analyses using a variety of mathematical methods, including some numerical methods. In particular, students should be able to:
a. Solve certain classes of first order ordinary differential equations (ODEs)
b. Find general solutions to second order ODEs (including special cases of inhomogeneous ODEs)
c. Find numerical solutions to first and second order initial value problems (IVPs) using Taylor's theorem,
d. Use Laplace transforms to analyse IVPs, particularly with discontinuous forcing,
e. Use and analyse systems of linear first order ODEs as models of systems with interactions
f. Classify 2nd order partial differential equations (PDEs) and numerically solve parabolic PDEs using finite differences.
3. Interpret the results of a mathematical model.
|Timetabled Learning Activities||Lectures: 3 x 1 hour per week; tutorials: 1 x 1 hour per week.|
|Unit Learning Experiences||Ideas are presented and illustrated in lectures with examples and motivation. Problems are derived from scratch to illustrate the thought process of modelling. These ideas are re-inforced in the tutorial/workshop setting with experienced practitioners guiding study. Self-directed learning and working together is emphasised in the assignments and worksheet components of the unit.|
|Assessment||Your ability to solve relevant mathematical problems will be assessed at regular intervals during the semester via assignments and a mid-semester test (internal only). These assessments are designed to allow you to demonstrate your ability in each of the content areas of the unit and to give you regular feedback on your progress, helping you to identify your areas of strength or weakness during the semester. Assignment solutions and results will be posted progressively on the Learning Management System.
The weightings for assessment items are as follows:
Assignments (4) - 20%
Mid-Semester Test - 15%
Final Examination - 65%
Assignments (4) - 30%
Final Examination - 70%
|Prerequisites||MAS182 Applied Mathematics or MAS161 Calculus and Matrix Algebra or equivalent.|
|Exclusions||Students may not enrol in this unit and MAS164 Fundamentals of Mathematics concurrently.|
|Appears in these Courses/Majors:
see individual structures for context
|Appears in these Co-Majors||Mathematics Minor Teaching Area
|Appears in these Minors||Applied and Computational Mathematics
Industrial and Applied Mathematics
|Internet Access Requirements||Murdoch units normally include an online component comprising materials, discussions, lecture recordings and assessment activities. All students, regardless of their location or mode of study, need to have access to and be able to use computing devices with browsing capability and a connection to the Internet via Broadband (Cable, ADSL or Mobile) or Wireless. The Internet connection should be readily available and allow large amounts of data to be streamed or downloaded (approximately 100MB per lecture recording). Students also need to be able to enter into online discussions and submit assignments online.|