University Course Planner The University of Adelaide Australia

APP MTH 3022 - Optimal Functions and Nanomechanics III

Career: Undergraduate
Units: 3
Term: Semester 2
Campus: North Terrace
Contact: Up to 3 contact hours per week
Available for Non-Award Study: Yes
Pre-Requisite: (MATHS 2101 and MATHS 2102) or (MATHS 2201 and MATHS 2202)
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
Incompatible: APP MTH 3010, APP MTH 3019
Assessment: Ongoing assessment 30%, Exam 70%
Syllabus:

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. Topic 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

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  Commonwealth Supported Student Contribution
Tuition Fees
Units EFTSL Pre-2010 2010 Onwards Domestic International
3 0.125 Band 2 $1,131 Band 2 $1,131 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
Semester 2 Mon 07/08/2017 Thu 31/08/2017 Fri 15/09/2017 Fri 27/10/2017


Class Details

Enrolment Class: Lecture
Class Nbr Section Size Available Dates Days Time Location
22233 LE01 35 16 24 Jul - 11 Sep Monday 3pm - 4pm Mawson, 134, Sprigg Room
25 Jul - 12 Sep Tuesday 4pm - 5pm Lower Napier, LG28, Lecture Theatre
27 Jul - 14 Sep Thursday 9am - 10am Lower Napier, LG28, Lecture Theatre
2 Oct - 23 Oct Monday 3pm - 4pm Mawson, 134, Sprigg Room
3 Oct - 24 Oct Tuesday 4pm - 5pm Lower Napier, LG28, Lecture Theatre
5 Oct - 26 Oct Thursday 9am - 10am Lower Napier, LG28, Lecture Theatre