Applied Mathematical Modelling (MAST30030)
Undergraduate level 3Points: 12.5On Campus (Parkville)
About this subject
Contact information
Semester 1
Dr Douglas Brumley
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 be able to:
- Evaluate the nature of deterministic mathematical modelling, including model formulation, selection of appropriate mathematical formalism, solution strategies and interpretation of results;
- Appraise contexts in which systems of autonomous ordinary differential equations or quasilinear first-order partial differential equations provide relevant models, and describe the general features of such models and what may be learned from them;
- Investigate and classify critical points in two-dimensional autonomous ODE problems, and be able to infer qualitative behaviour in the phase plane.
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: 4 March 2025
Eligibility and requirements
Prerequisites
| Code | Name | Teaching period | Credit Points |
|---|---|---|---|
| MAST20030 | Differential Equations | Semester 2 (On Campus - Parkville) |
12.5 |
One of
| Code | Name | Teaching period | Credit Points |
|---|---|---|---|
| MAST20009 | Vector Calculus |
Semester 2 (On Campus - Parkville)
Semester 1 (On Campus - Parkville)
|
12.5 |
| MAST20032 | Vector Calculus: Advanced | Semester 1 (On Campus - Parkville) |
12.5 |
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: 4 March 2025
Assessment
| Description | Timing | Percentage |
|---|---|---|
Three written assignments, due at regular intervals during semester
| Throughout the semester | 30% |
Written examination
| During the examination period | 70% |
Last updated: 4 March 2025
Dates & times
- Semester 1
Coordinator Douglas Brumley 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 3 March 2025 to 1 June 2025 Last self-enrol date 14 March 2025 Census date 31 March 2025 Last date to withdraw without fail 9 May 2025 Assessment period ends 27 June 2025 Semester 1 contact information
Dr Douglas Brumley
Time commitment details
170 hours
What do these dates mean
Visit this webpage to find out about these key dates, including how they impact on:
- Your tuition fees, academic transcript and statements.
- And for Commonwealth Supported students, your:
- Student Learning Entitlement. This applies to all students enrolled in a Commonwealth Supported Place (CSP).
Subjects withdrawn after the census date (including up to the ‘last day to withdraw without fail’) count toward the Student Learning Entitlement.
Last updated: 4 March 2025
Further information
- Texts
- Related Handbook entries
This subject contributes to the following:
Type Name Informal specialisation Science Discipline subjects - new generation B-SCI Informal specialisation Applied Mathematics Informal specialisation Applied Mathematics specialisation 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: 4 March 2025