Partial differential equations (PDEs) are arise in many areas of applied mathematics; whenever a problem changes continuously in space and in time as, for example, in fluid flow or a description of the spread of a virus, PDEs are inevitably required to describe the system. In general PDEs are very hard to solve analytically, but there are a number of equations that recur often and for which techniques of solution have been found. In this unit we discuss several of these, and indicate the flavours of PDEs that occur fin applied mathematics, physics, biological science, commerce, and engineering.
Topics discussed include: First-order PDEs: the linear wave equation, method of characteristics, traffic flow models, wave breaking, and shocks. Second-order PDEs: Classification of PDEs and characteristic curves; parabolic, elliptic, and hyperbolic equations; initial and boundary value problems; separation of variables techniques; D'Alembert's solution; orthogonal functions and Sturm-Liouville theory; fundamental solutions and Green's functions
|Unit name||Partial Differential Equations, Applications and Methods 3|
|College/School||College of Sciences and Engineering
School of Natural Sciences
|Coordinator||Professor Andrew Bassom|
|Available as student elective?||Yes|
|Delivered By||University of Tasmania|
|Location||Study period||Attendance options||Available to|
- International students
- Domestic students
Please check that your computer meets the minimum System Requirements if you are attending via Distance/Off-Campus.
Units are offered in attending mode unless otherwise indicated (that is attendance is required at the campus identified). A unit identified as offered by distance, that is there is no requirement for attendance, is identified with a nominal enrolment campus. A unit offered to both attending students and by distance from the same campus is identified as having both modes of study.
|Study Period||Start date||Census date||WW date||End date|
* The Final WW Date is the final date from which you can withdraw from the unit without academic penalty, however you will still incur a financial liability (refer to How do I withdraw from a unit? for more information).
Unit census dates currently displaying for 2022 are indicative and subject to change. Finalised census dates for 2022 will be available from the 1st October 2021. Note census date cutoff is 11.59pm AEST (AEDT during October to March).
- Explain the nature and classification of linear, semi-linear, quasi-linear homogeneous or inhomogeneous, elliptic, parabolic or hyperbolic boundary and initial value problems.
- Use appropriate solution techniques to solve first and second order partial differential equations
- Learn how to adapt and refine the various standard solution techniques to enable solution of more intricate types of problem
- Clearly communicate and present findings in written form using appropriate mathematical terminology combined with good explanation
|Field of Education||Commencing Student Contribution 1||Grandfathered Student Contribution 1||Approved Pathway Course Student Contribution 2||Domestic Full Fee|
1 Please refer to more information on student contribution amounts.
2 Please refer to more information on eligibility and Approved Pathway courses.
3 Please refer to more information on eligibility for HECS-HELP.
4 Please refer to more information on eligibility for FEE-HELP.
Please note: international students should refer to What is an indicative Fee? to get an indicative course cost.
PrerequisitesAdmission into a Masters course OR KMA252 Calculus and Applications 2 OR KME271 Engineering Mathematics
3 x 1-hr lectures, 1 x 1-hr tutorial weekly
|Assessment||Mid semester test (20%)|Final exam (40%)|5 fortnightly assignments (40%)|
|Timetable||View the lecture timetable | View the full unit timetable|
Required readings will be listed in the unit outline prior to the start of classes.
|Links||Booktopia textbook finder|
The University reserves the right to amend or remove courses and unit availabilities, as appropriate.