University Course Planner The University of Adelaide Australia

APP MTH 3022 - Optimal Functions and Nanomechanics III

Career: Undergraduate
Units: 3
Term: 3920
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 2102 or MATHS 2106 or MATHS 2201) and (MATHS 2101 or MATHS 2202 or ELEC ENG 2106)
Assumed Knowledge: Basic computer programming skills such as would be obtained from ENG 1002 or 1003 or COMP SCI 1012 or a MATHS or APP MTHS course with a computational component in MATLAB
Assessment: Ongoing assessment, Exam
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. 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.

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Undergraduate
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Units
EFTSL
Amount
3
0.125
          
  


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
3920 Mon 12/08/2019 Sat 31/08/2019 Fri 20/09/2019 Fri 01/11/2019


Class Details

Enrolment Class: Lecture
Class Nbr Section Size Available Dates Days Time Location
22104 LE01 25 8 29 Jul - 16 Sep Monday 2pm - 3pm Napier, G03, Lecture Theatre
31 Jul - 18 Sep Wednesday 3pm - 4pm Engineering Sth, S112, Teaching Room
2 Aug - 20 Sep Friday 12pm - 1pm Lower Napier, LG29, Lecture Theatre
7 Oct - 28 Oct Monday 2pm - 3pm Napier, G03, Lecture Theatre
9 Oct - 30 Oct Wednesday 3pm - 4pm Engineering Sth, S112, Teaching Room
11 Oct - 1 Nov Friday 12pm - 1pm Lower Napier, LG29, Lecture Theatre