APP MTH 4122 - Optimal Functions and Nanomechanics - Honours
Career: | Undergraduate |
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Units: | 3 |
Term: | 3920 |
Campus: | North Terrace |
Contact: | Up to 3 contact hours per week |
Restriction: | Honours students only |
Available for Study Abroad and Exchange: | Yes |
Available for Non-Award Study: | No |
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. 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
Study Abroad student tuition fees are available here
Only some Postgraduate Coursework programs are available as Commonwealth Supported. Please check your program for specific fee information.
The fees displayed below for international students are for students commencing a program in 2024 only. International students who commenced a program in 2023 or prior can find their fee here.
EFTSL | |||
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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 |
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3920 | Mon 12/08/2019 | Sat 31/08/2019 | Fri 20/09/2019 | Fri 01/11/2019 |
Class Details
Enrolment Class: Lecture | |||||||
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Class Nbr | Section | Size | Available | Dates | Days | Time | Location |
20084 | LE01 | 4 | 3 | 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 |