mat4pde nonlinear pde
NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS
MAT4PDE
2016
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.
SchoolSchool Engineering&Mathematical Sciences
Credit points15
Subject Co-ordinatorPhilip Broadbridge
Available to Study Abroad StudentsYes
Subject year levelYear Level 4 - UG/Hons/1st Yr PG
Exchange StudentsYes
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
Special conditionsN/A
Graduate capabilities & intended learning outcomes
01. Demonstrate method of characteristics for solving first-order and second-order nonlinear wave equations.
- Activities:
- Interactive lectures and text-book research guided by assignments.
- Related graduate capabilities and elements:
- Literacies and Communication Skills(Writing,Speaking,Quantitative Literacy)
- Literacies and Communication Skills(Writing,Speaking,Quantitative Literacy)
- Literacies and Communication Skills(Writing,Speaking,Quantitative Literacy)
- Inquiry and Analytical Skills(Critical Thinking,Creative Problem-solving,Inquiry/Research)
- Inquiry and Analytical Skills(Critical Thinking,Creative Problem-solving,Inquiry/Research)
- Inquiry and Analytical Skills(Critical Thinking,Creative Problem-solving,Inquiry/Research)
- Discipline -Specific Knowledge and Skills(Discipline-Specific Knowledge and Skills)
02. Solve Burgers' equation with standard boundary conditions, relate these to the travelling wave solution and the viscosity solution of inviscid Burgers' equation
- Activities:
- Interactive lectures and text-book research guided by assignments.
- Related graduate capabilities and elements:
- Literacies and Communication Skills(Writing,Speaking,Quantitative Literacy)
- Literacies and Communication Skills(Writing,Speaking,Quantitative Literacy)
- Literacies and Communication Skills(Writing,Speaking,Quantitative Literacy)
- Inquiry and Analytical Skills(Critical Thinking,Creative Problem-solving,Inquiry/Research)
- Inquiry and Analytical Skills(Critical Thinking,Creative Problem-solving,Inquiry/Research)
- Inquiry and Analytical Skills(Critical Thinking,Creative Problem-solving,Inquiry/Research)
- Discipline -Specific Knowledge and Skills(Discipline-Specific Knowledge and Skills)
03. Construct entropy measures for nonlinear diffusion equations.
- Activities:
- Interactive lectures and text-book research guided by assignments.
- Related graduate capabilities and elements:
- Literacies and Communication Skills(Writing,Speaking,Quantitative Literacy)
- Literacies and Communication Skills(Writing,Speaking,Quantitative Literacy)
- Inquiry and Analytical Skills(Critical Thinking,Creative Problem-solving,Inquiry/Research)
- Inquiry and Analytical Skills(Critical Thinking,Creative Problem-solving,Inquiry/Research)
- Inquiry and Analytical Skills(Critical Thinking,Creative Problem-solving,Inquiry/Research)
- Discipline -Specific Knowledge and Skills(Discipline-Specific Knowledge and Skills)
04. Solve nonlinear boundary value problems for diffusion equations.
- Activities:
- Interactive lectures and text-book research guided by assignments.
- Related graduate capabilities and elements:
- Literacies and Communication Skills(Writing,Speaking,Quantitative Literacy)
- Literacies and Communication Skills(Writing,Speaking,Quantitative Literacy)
- Inquiry and Analytical Skills(Critical Thinking,Creative Problem-solving,Inquiry/Research)
- Inquiry and Analytical Skills(Critical Thinking,Creative Problem-solving,Inquiry/Research)
- Inquiry and Analytical Skills(Critical Thinking,Creative Problem-solving,Inquiry/Research)
- Discipline -Specific Knowledge and Skills(Discipline-Specific Knowledge and Skills)
05. Distinguish nonlinear dynamical behaviour from linear dynamical behaviour.
- Activities:
- Interactive lectures and text-book research guided by assignments. Student seminars.
- Related graduate capabilities and elements:
- Literacies and Communication Skills(Writing,Speaking,Quantitative Literacy)
- Literacies and Communication Skills(Writing,Speaking,Quantitative Literacy)
- Inquiry and Analytical Skills(Critical Thinking,Creative Problem-solving,Inquiry/Research)
- Inquiry and Analytical Skills(Critical Thinking,Creative Problem-solving,Inquiry/Research)
- Discipline -Specific Knowledge and Skills(Discipline-Specific Knowledge and Skills)
06. Recognize the role of women and various cultures in the science of nonlinear partial differential equations.
- Activities:
- Biographical notes in lectures Student seminars.
- Related graduate capabilities and elements:
- Literacies and Communication Skills(Writing,Speaking,Quantitative Literacy)
- Inquiry and Analytical Skills(Critical Thinking,Creative Problem-solving,Inquiry/Research)
Subject options
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Melbourne, 2016, Semester 1, Day
Overview
Online enrolmentYes
Maximum enrolment sizeN/A
Enrolment information
Subject Instance Co-ordinatorPhilip Broadbridge
Class requirements
LectureWeek: 10 - 22
Two 1.0 hours lecture per week on weekdays during the day from week 10 to week 22 and delivered via face-to-face.
Assessments
| Assessment element | Comments | % | ILO* |
|---|---|---|---|
| 2-hour exam | Alternative weightings for assessment items may be negotiated with the subject coordinator. | 50 | 01, 02, 03, 04 |
| 2 assignments | 30 | 01, 02, 03, 04, 05 | |
| 3rd assignment | 10 | 01, 02, 03, 04, 05 | |
| 15 min seminar | 10 | 05, 06 |