Partial Differential Equations, Applications and Methods 3 unit (KMA354)

Introduction

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

Summary

Unit name	Partial Differential Equations, Applications and Methods 3
Unit code	KMA354
Credit points	12.5
College/School	Sciences and Engineering School of Natural Sciences
Discipline	Mathematics
Coordinator	Professor Andrew Bassom
Available as an elective?	Yes
Delivered By	University of Tasmania
Level	Advanced

Availability

Specific information on 2027 unit availability will be available in August

Learning Outcomes

• 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

Fee Information

2027 fee information will be available in August.

Requisites

Prerequisites

KMA252 Calculus and Applications 2 OR KME271 Engineering Mathematics

Teaching

Teaching Pattern	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

Textbooks

Required	Required readings will be listed in the unit outline prior to the start of classes.

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