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Computational Differential Equations (MAST90026)
Graduate courseworkPoints: 12.5Not available in 2017
Overview
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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
Additional details
Weekly homework for the first four weeks (20%); up to 60 pages of written assignments (60%: three assignments worth 20% each due mid and late in semester); a 15-minute oral presentation on a project (20%) held towards the end of semester.
Last updated: 3 November 2022
Dates & times
Not available in 2017
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 Doctor of Philosophy - Engineering Course Master of Philosophy - Engineering Course Ph.D.- 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.
Entry requirements including prerequisites may apply. Please refer to the CAP applications page for further information.
Last updated: 3 November 2022