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 an elective?||Yes|
|Delivered By||University of Tasmania|
|Location||Study period||Attendance options||Available to|
- International students
- Domestic students
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|Study Period||Start date||Census date||WW date||End date|
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- 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
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PrerequisitesKMA252 Calculus and Applications 2 OR KME271 Engineering Mathematics
3 x 1-hr lectures, 1 x 1-hr tutorial weekly
|Assessment||Mid semester test (20%)|5 fortnightly assignments (40%)|Final exam (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|
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