Variational Calculus

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)

Corequisite(s)

Nil

Teaching method

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

Assessment

Assignment 1, Assignment 2, Examination

Fees

EFTSL*: 0.125
Commonwealth Supported program (Band 2)
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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
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* 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.