NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS
MAT4PDE
2021
Credit points: 15
Subject outline
Many quantities of practical interest in continuum mechanics, environmental mechanics and population ecology, are commonly represented as smooth functions of space and time that are governed by nonlinear partial differential equations. Such equations arise also in differential geometry of smooth manifolds. Some understanding of nonlinear partial differential equations is considered to be essential for any further development of applicable analysis or continuum geometry, with impacts on many other branches of mathematics, physics, chemistry, finance and biology. Topics covered include (i) local formulation of conservation laws, (ii) classical and weak solutions of hyperbolic, parabolic and elliptic equations, (iii) method of characteristics (iv) viscosity solutions of Burgers' equation, (v) reversible and irreversible processes, (vi) integrable nonlinear diffusion equations, (vii) curvature-driven flows, (viii) reaction-diffusion equations and (ix) solitons.
SchoolEngineering and Mathematical Sciences
Credit points15
Subject Co-ordinatorLuke Prendergast
Available to Study Abroad/Exchange StudentsYes
Subject year levelYear Level 4 - UG/Hons/1st Yr PG
Available as ElectiveNo
Learning ActivitiesN/A
Capstone subjectNo
Subject particulars
Subject rules
Prerequisites MAT2VCA and 30 credit points of 3rd year Mathematics subjects (MAT3 or STM3)
Co-requisitesN/A
Incompatible subjectsN/A
Equivalent subjectsN/A
Quota Management StrategyN/A
Quota-conditions or rulesN/A
Special conditionsN/A
Minimum credit point requirementN/A
Assumed knowledgeN/A
Career Ready
Career-focusedNo
Work-based learningNo
Self sourced or Uni sourcedN/A
Entire subject or partial subjectN/A
Total hours/days requiredN/A
Location of WBL activity (region)N/A
WBL addtional requirementsN/A
Graduate capabilities & intended learning outcomes
Graduate Capabilities
Intended Learning Outcomes
Subject options
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Melbourne (Bundoora), 2021, Semester 1, Day
Overview
Online enrolmentNo
Maximum enrolment sizeN/A
Subject Instance Co-ordinatorLuke Prendergast
Class requirements
LectureWeek: 10 - 22
Two 1.00 hour lecture per week on weekdays during the day from week 10 to week 22 and delivered via face-to-face.
Assessments
| Assessment element | Category | Contribution | Hurdle | % | ILO* |
|---|---|---|---|---|---|
| 2-hour exam (approx. 3000 words) Alternative weightings for assessment items may be negotiated with the subject coordinator. | N/A | N/A | No | 50 | SILO1, SILO2, SILO3, SILO4 |
| 2 assignments (approx. 750 words each) | N/A | N/A | No | 30 | SILO1, SILO2, SILO3, SILO4, SILO5 |
| 3rd assignment (approx. 750 words) | N/A | N/A | No | 10 | SILO1, SILO2, SILO3, SILO4, SILO5 |
| 15 min seminar (equivalent to 750 words) | N/A | N/A | No | 10 | SILO5, SILO6 |