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Area/Catalogue
MATH 3036

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Course Level
Undergraduate

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Offered Externally
No

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Course ID
106060

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Unit Value
4.5

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University-wide elective course
No

Course owner

Course owner
School of Information Technology and Mathematical Sciences

Course aim

This course aims to introduce the theory of the calculus of variations, which is motivated by applications to problems in physics and engineering. The theoretical development is quite extensive, covering both scalar and vector functionals of real and vector variables, and the cases of both fixed and free boundaries and free and constrained problems. Many examples illustrating the theoretical concepts are taken from the discipline of mechanics.

Course content

The variational integral and functionals of one dependent and one independent variable; fundamental principles of the variational method and the Euler equations; generalisations to two or more dependent and/or independent variables; variation subject to constraints; Lagrange multipliers; boundary conditions: natural boundary conditions and free boundaries; the second variation and the concept of stability (optional); Hamilton’s principle, the equations of classical mechanics and Lagrange’s equations; applications to problems in mechanics appear throughout the course.

Textbook(s)

G. B. Arfken and H. J. Weber 2007, Mathematical Methods for Physicists, 6th edn, Academic Press

Prerequisite(s)

Common to all relevant programs
Subject Area & Catalogue Number Course Name
MATH 2026 Calculus 3

Corequisite(s)

Nil

Teaching method

Component Duration
INTERNAL, MAWSON LAKES
Lecture 4 hrs (2x2 hrs) x 13 weeks

Note: These components may or may not be scheduled in every study period. Please refer to the timetable for further details.


Assessment

Task Length Weighting Duration
INTERNAL, MAWSON LAKES
Assignment 1 1250 word equivalent 20% N/A
Assignment 2 1250 word equivalent 20% N/A
Examination 2000 word equivalent 60% N/A

Fees

EFTSL*: 0.125
Commonwealth Supported program (Band 2)
To determine the fee for this course as part of a Commonwealth Supported program, go to:
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Fee-paying program for domestic and international students
International students and students undertaking this course as part of a postgraduate fee paying program must refer to the relevant program home page to determine the cost for undertaking this course.

Non-award enrolment
Non-award tuition fees are set by the university. To determine the cost of this course, go to:
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Not all courses are available on all of the above bases, and students must check to ensure that they are permitted to enrol in a particular course.

* Equivalent Full Time Study Load. Please note all EFTSL values are published and calculated at ten decimal places. Values are displayed to three decimal places for ease of interpretation

Course Coordinators

School of Information Technology and Mathematical

Degrees this course is offered in

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