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

Hobart

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

Location	Study period	Attendance options		Available to
Hobart	Semester 2

Note

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.

Key Dates

Study Period	Start date	Census date	WW date	End date
Semester 2	5/7/2026	27/7/2026	30/8/2026	24/10/2026

* 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 2026 are indicative and subject to change. Finalised census dates for 2026 will be available from the 1st October 2025. Note census date cutoff is 11.59pm AEST (AEDT during October to March).

About Census Dates

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

Field of Education	Commencing Student Contribution 1,3	Grandfathered Student Contribution 1,3	Approved Pathway Course Student Contribution 2,3	Domestic Full Fee 4
010101	$592.00	$592.00	not applicable	$2,919.00

• Available as a Commonwealth Supported Place
• HECS-HELP is available on this unit, depending on your eligibility³
• FEE-HELP is available on this unit, depending on your eligibility⁴

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.

If you have any questions in relation to the fees, please contact UniConnect or more information is available on StudyAssist.

Please note: international students should refer to What is an indicative Fee? to get an indicative course cost.

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.

The University reserves the right to amend or remove courses and unit availabilities, as appropriate.