University Course Planner The University of Adelaide Australia

APP MTH 3022 - Optimal Functions and Nanomechanics III

Career: Undergraduate
Units: 3
Term: 3820
Campus: North Terrace
Contact: Up to 3 contact hours per week
Available for Study Abroad and Exchange: Yes
Available for Non-Award Study: Yes
Pre-Requisite: (MATHS 2101 or MATHS 2202) and (MATHS 2102 or MATHS 2201)
Assumed Knowledge: Basic computer programming skills such as would be obtained from COMP SCI 1012, 1101, MECH ENG 1100, 1102, 1103, 1104, 1105, C&ENVENG 1012
Assessment: Ongoing assessment, Exam

Many problems in the sciences and engineering seek to find a shape or function that minimises or maximises some quantity. For example, an engineer may design a yacht's hull to minimise drag. And in nature, the shape that a complicated protein might adopt is determined in part by the lowest-energy state available to the protein during the folding process. The Calculus of Variations extends familiar calculus techniques to answer questions regarding optimal geometry or functions. The Calculus of Variations is applicable to almost all continuous physical systems, ranging through elasticity, solid and fluid mechanics, electro-magnetism, gravitation, quantum mechanics and string theory. In this course we will consider, in particular, problems from Nanoscience. Nanoscience is a multidisciplinary field at the nexus of physics, chemistry and engineering. Materials and systems that may be very well understood at the macroscale can often exhibit surprising phenomena at the nanoscale. Topics covered are: Classical Calculus of Variations problems such as the geodesic, catenary and brachistochrone; derivation and use of the Euler-Lagrange equations; multiple dependent variables (Hamilton's equations) and multiple independent variables (minimal surfaces); constrained problems, problems with variable end points and those with non-integral constraints; conservation laws and Noether's theorem; computational solutions using Euler's finite difference and Rayleigh-Ritz methods. Many of the examples considered will draw from continuum modelling of the intermolecular interaction potential utilizing special functions (such as gamma, beta, hypergeometric and generalized hypergeometric functions of two variables) and by application of Euler's elastica.

Course Fees

Course fees are displayed for the Program: select program

Study Abroad student tuition fees available here

Only some Postgraduate Coursework programs are available as Commonwealth Supported. Please check your program for specific fee information

  Commonwealth Supported Student Contribution
Tuition Fees
Units EFTSL Pre-2010 2010 Onwards Domestic International
3 0.125 Band 2 $1,169 Band 2 $1,169 select program select program

Course Outline

A Course Outline which includes Learning Outcomes, Learning Resources, Learning & Teaching for this course may be accessed here

Critical Dates

Term Last Day to Add Online Census Date Last Day to WNF Last Day to WF
3820 Mon 06/08/2018 Fri 31/08/2018 Fri 14/09/2018 Fri 26/10/2018

Class Details

Enrolment Class: Lecture
Class Nbr Section Size Available Dates Days Time Location
22099 LE01 25 7 23 Jul - 10 Sep Monday 3pm - 4pm Barr Smith South, 3022, Polygon Lecture Theatre
26 Jul - 13 Sep Thursday 11am - 12pm Barr Smith South, 3022, Polygon Lecture Theatre
27 Jul - 14 Sep Friday 11am - 12pm Marjoribanks, 126, SANTOS Lecture Theatre
1 Oct - 22 Oct Monday 3pm - 4pm Barr Smith South, 3022, Polygon Lecture Theatre
4 Oct - 25 Oct Thursday 11am - 12pm Barr Smith South, 3022, Polygon Lecture Theatre
5 Oct - 26 Oct Friday 11am - 12pm Marjoribanks, 126, SANTOS Lecture Theatre