Courses & Units

Partial Differential Equations, Applications and Methods 3 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 College of Sciences and Engineering
School of Natural Sciences
Discipline Mathematics
Coordinator Professor Andrew Bassom
Available as student elective? Yes
Delivered By University of Tasmania
Level Advanced

Availability

Location Study period Attendance options Available to
Hobart Semester 2 On-Campus International Domestic

Key

On-campus
Off-Campus
International students
Domestic students
Note

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Key Dates

Study Period Start date Census date WW date End date
Semester 2 11/7/2022 9/8/2022 29/8/2022 16/10/2022

* 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).

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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
Field of Education Commencing Student Contribution 1 Grandfathered Student Contribution 1 Approved Pathway Course Student Contribution 2 Domestic Full Fee
010101 $498.00 $498.00 not applicable $2,402.00

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.

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Requisites

Prerequisites

Admission into a Masters course OR KMA252 Calculus and Applications 2 OR KME271 Engineering Mathematics

Teaching

Teaching Pattern

3 x 1-hr lectures, 1 x 1-hr tutorial weekly

AssessmentMid semester test (20%)|Final exam (40%)|5 fortnightly assignments (40%)
TimetableView 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.

LinksBooktopia textbook finder

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