NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS

MAT4PDE

2020

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.

School: Engineering and Mathematical Sciences (Pre 2022)

Credit points: 15

Subject Co-ordinator: Joel Miller

Available to Study Abroad/Exchange Students: Yes

Subject year level: Year Level 4 - UG/Hons/1st Yr PG

Exchange Students: No

Available as Elective: No

Learning Activities: N/A

Capstone subject: No

Subject particulars

Subject rules

Prerequisites: MAT2VCA and 30 credit points of 3rd year Mathematics subjects (MAT3 or STM3)

Co-requisites: N/A

Incompatible subjects: N/A

Equivalent subjects: N/A

Quota Management Strategy: N/A

Quota-conditions or rules: N/A

Special conditions: N/A

Minimum credit point requirement: N/A

Assumed knowledge: N/A

Career Ready

Career-focused: No

Work-based learning: No

Self sourced or Uni sourced: N/A

Entire subject or partial subject: N/A

Total hours/days required: N/A

Location of WBL activity (region): N/A

WBL addtional requirements: N/A

Graduate capabilities & intended learning outcomes

Graduate Capabilities

COMMUNICATION - Communicating and Influencing

DISCIPLINE KNOWLEDGE AND SKILLS

INQUIRY AND ANALYSIS - Creativity and Innovation

INQUIRY AND ANALYSIS - Critical Thinking and Problem Solving

INQUIRY AND ANALYSIS - Research and Evidence-Based Inquiry

Intended Learning Outcomes

01. Demonstrate method of characteristics for solving first-order and second-order nonlinear wave equations.

02. Solve Burgers' equation with standard boundary conditions, relate these to the travelling wave solution and the viscosity solution of inviscid Burgers' equation

03. Construct entropy measures for nonlinear diffusion equations.

04. Solve nonlinear boundary value problems for diffusion equations.

05. Distinguish nonlinear dynamical behaviour from linear dynamical behaviour.

06. Recognise the role of women and various cultures in the science of nonlinear partial differential equations.

Melbourne (Bundoora), 2020, Semester 1, Day

Overview

Online enrolment: No

Maximum enrolment size: N/A

Enrolment information: N/A

Subject Instance Co-ordinator: Joel Miller

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	Comments	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	N/A	No	50	SILO1, SILO2, SILO3, SILO4
2 assignments (approx. 750 words each)	N/A	N/A	N/A	No	30	SILO1, SILO2, SILO3, SILO4, SILO5
3rd assignment (approx. 750 words)	N/A	N/A	N/A	No	10	SILO1, SILO2, SILO3, SILO4, SILO5
15 min seminar (equivalent to 750 words)	N/A	N/A	N/A	No	10	SILO5, SILO6