Computational Differential Equations (MAST90026)
Graduate courseworkPoints: 12.5On Campus (Parkville)
For information about the University’s phased return to campus and in-person activity in Winter and Semester 2, please refer to the on-campus subjects page.
Please refer to the LMS for up-to-date subject information, including assessment and participation requirements, for subjects being offered in 2020.
Overview
| Availability | Semester 1 |
|---|---|
| Fees | Look up fees |
Many processes in the natural sciences, engineering and finance are described mathematically using ordinary or partial differential equations. Only the simplest or those with special structure can be solved exactly. This subject discusses common techniques for computing numerical solutions to differential equations and introduces the major themes of accuracy, stability and efficiency. Understanding these basic properties of scientific computing algorithms should prevent the unwary from using software packages inappropriately or uncritically, and provide a foundation for devising methods for nonstandard problems. We cover both time-independent problems, in one and higher space dimensions, and evolution equations of hyperbolic or parabolic type.
Intended learning outcomes
After completing this subject, students should:
- appreciate how and why numerical methods are developed to solve differential equations commonly arising in finance, science and engineering;
- understand the chief factors to be considered in choosing an appropriate algorithm for a given class of problem;
- acquire high level numerical tools and knowledge that can be used to solve a range of problems in science and engineering;
- gain the ability to pursue further studies in this and related areas.
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:
- problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies;
- 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;
- collaborative skills: the ability to work in a team;
- time-management skills: the ability to meet regular deadlines while balancing competing commitments.
Last updated: 3 November 2022
Eligibility and requirements
Prerequisites
Students should be able to program in one of: C, Matlab, Mathematica, Perl, Fortran, Python etc
Corequisites
None
Non-allowed subjects
None
Recommended background knowledge
Students are required to write programs in MATLAB so previous experience in writing and debugging procedural computer programs is expected. It is recommended that students have completed a subject in partial differential equations.
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
Due to the impact of COVID-19, assessment may differ from that published in the Handbook. Students are reminded to check the subject assessment requirements published in the subject outline on the LMS
| Description | Timing | Percentage |
|---|---|---|
Weekly homework for the first four weeks | Early in the teaching period | 20% |
Up to 60 pages of written assignments (three assignments worth 20% each due mid and late in semester)
| Second half of the teaching period | 60% |
An oral presentation on a project held towards the end of semester
| Second half of the teaching period | 20% |
Last updated: 3 November 2022
Dates & times
- Semester 1
Principal coordinator Hailong Guo Mode of delivery On Campus (Parkville) Contact hours 36 total, comprising one one-hour and one two-hour computer lab per week Total time commitment 170 hours Teaching period 2 March 2020 to 7 June 2020 Last self-enrol date 13 March 2020 Census date 30 April 2020 Last date to withdraw without fail 5 June 2020 Assessment period ends 3 July 2020 Semester 1 contact information
Time commitment details
170 hours
Last updated: 3 November 2022
Further information
- Texts
Prescribed texts
TBA
Recommended texts and other resources
R.J.Leveque, Finite difference methods for ordinary and partial differential equations. Steady-state and time-dependent problems, SIAM, 2007.
A. Iserles, A First Course in the Numerical Analysis of Differential Equations, 2nd edn, Cambridge University Press, 2008. - Related Handbook entries
This subject contributes to the following:
Type Name Course Master of Science (Mathematics and Statistics) Course Ph.D.- Engineering Course Doctor of Philosophy - Engineering Course Master of Philosophy - Engineering Informal specialisation Mathematics and Statistics - 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