Applied Mathematical Modelling (MAST30030)
Undergraduate level 3Points: 12.5On Campus (Parkville)
Overview
| Availability | Semester 1 |
|---|---|
| Fees | Look up fees |
This subject demonstrates how the mathematical modelling process naturally gives rise to certain classes of ordinary and partial differential equations in many contexts, including the infectious diseases, the flow of traffic and the dynamics of particles and of fluids. It advances the student’s knowledge of the modelling process, as well addressing important mathematical ideas in deterministic modelling and the challenges raised by system nonlinearity.
- Infectious disease models and other contexts leading to systems of autonomous first-order differential equations; initial value problem, phase space, critical points, local linearization and stability; qualitative behaviour of plane autonomous systems, structural stability; formulation, interpretation and critique of models.
- Conservation laws and flux functions leading to first-order quasilinear-linear partial differential equations; characteristics, fans, shocks and applications including modelling traffic flow.
- Introduction to continuum mechanics: basic principles; tensor algebra and tensor calculus; the ideal fluid model and potential flow; the Newtonian fluid, Navier-Stokes equations and simple solutions.
Intended learning outcomes
On completion of this subject, students should:
- understand the nature of deterministic mathematical modelling, including model formulation, selection of appropriate mathematical formalism, solution strategies and interpretation of results;
- know contexts in which systems of autonomous ordinary differential equations or quasilinear first-order partial differential equations provide relevant models and appreciate general features of such models and what may be learned from them;
- be able to find and classify critical points in two-dimensional autonomous ODE problems, and be able to infer qualitative behaviour in the phase plane;
- be able to solve quasilinear PDEs in two variables using the method of characteristics, including the construction of weak solutions (fans and shocks);
- understand the fundamental principles of classical continuum mechanics and develop facility in related vector and tensor analysis;
- understand the assumptions underlying the ideal fluid model and the Newtonian fluid model and be able to find and interpret solutions for simple flows.
Generic skills
In addition to learning specific skills that will assist students in their future careers in science, they will have the opportunity to develop generic skills that will assist them in any future career path. These include:
- mathematical modelling skills: the ability to formulate a mathematical model, select an appropriate solution strategy and interpret solutions;
- analytical skills: the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis;
- time-management skills: the ability to meet regular deadlines while balancing competing commitments.
Last updated: 3 November 2022
Eligibility and requirements
Prerequisites
| Code | Name | Teaching period | Credit Points |
|---|---|---|---|
| MAST20009 | Vector Calculus |
Semester 1 (On Campus - Parkville)
Semester 2 (On Campus - Parkville)
|
12.5 |
plus one of
| Code | Name | Teaching period | Credit Points |
|---|---|---|---|
| MAST20030 | Differential Equations | Semester 2 (On Campus - Parkville) |
12.5 |
| MAST20029 | Engineering Mathematics |
Semester 1 (On Campus - Parkville)
Semester 2 (On Campus - Parkville)
Summer Term (On Campus - Parkville)
|
12.5 |
MAST30029 Partial Differential Equations (prior to 2014)
(MAST20029 Engineering Mathematics must have a result grade of H2A or above)
Corequisites
None
Non-allowed subjects
None
Inherent requirements (core participation requirements)
The University of Melbourne is committed to providing students with reasonable adjustments to assessment and participation under the Disability Standards for Education (2005), and the Assessment and Results Policy (MPF1326). Students are expected to meet the core participation requirements for their course. These can be viewed under Entry and Participation Requirements for the course outlines in the Handbook.
Further details on how to seek academic adjustments can be found on the Student Equity and Disability Support website: http://services.unimelb.edu.au/student-equity/home
Last updated: 3 November 2022
Assessment
Additional details
Three written assignments amounting to a total of up to 50 pages, due at regular intervals during semester (30%); 3-hour written examination in the examination period (70%)
Last updated: 3 November 2022
Dates & times
- Semester 1
Principal coordinator John Sader Mode of delivery On Campus (Parkville) Contact hours 36 one-hour lectures (three per week); 12 one-hour practice classes (one per week) Total time commitment 170 hours Teaching period 27 February 2017 to 28 May 2017 Last self-enrol date 10 March 2017 Census date 31 March 2017 Last date to withdraw without fail 5 May 2017 Assessment period ends 23 June 2017 Semester 1 contact information
Email: jsader@unimelb.edu.au
Time commitment details
170 hours
Last updated: 3 November 2022
Further information
- Texts
- Related Handbook entries
This subject contributes to the following:
Type Name Informal specialisation Applied Mathematics Informal specialisation Applied Mathematics Informal specialisation Science-credited subjects - new generation B-SCI and B-ENG. Informal specialisation Selective subjects for B-BMED Major Applied Mathematics Informal specialisation Applied Mathematics - Available through the Community Access Program
About the Community Access Program (CAP)
This subject is available through the Community Access Program (also called Single Subject Studies) which allows you to enrol in single subjects offered by the University of Melbourne, without the commitment required to complete a whole degree.
Please note Single Subject Studies via Community Access Program is not available to student visa holders or applicants
Entry requirements including prerequisites may apply. Please refer to the CAP applications page for further information.
- Available to Study Abroad and/or Study Exchange Students
Last updated: 3 November 2022