Courses & Units

Calculus of Variations KMA381


Offered in even numbered years only. Offered subject to student demand/lecturer availability


This unit gives an introduction to Calculus of Variations and its use in optimal control theory. Review of basic multi-variable calculus, constrained maxima and minima, Lagrange multipliers. The "simplest problem" of the Calculus of Variations. The Euler-Lagrange equation. Application to classical problems in geometry and physics. Isoperimetric problems, the "brachistochrone". Geodesics. Application to problems in several unknown functions and generalization to higher derivatives. Propagation of light rays in 3D space, minimum surfaces. Constrained variational problems. Use of Lagrange multipliers. Variable end conditions. Application to Mechanics and Physics. Energy and Hamilton's principle. Generalized coordinates. Motion of a simple pendulum. The vibrating string. The vibrating elastic rod. Direct Methods. The Ritz method. Minimizing sequences. Eigenvalue problems. Galerkin methods. The control problem. Optimal control. Pontryagin's principle.


Unit name Calculus of Variations
Unit code KMA381
Credit points 12.5
Faculty/School College of Sciences and Engineering
School of Natural Sciences
Discipline Mathematics
Teaching staff

Prof L Forbes

Level Advanced
Available as student elective? Yes
Breadth Unit? No


This unit is currently unavailable.


Please check that your computer meets the minimum System Requirements if you are attending via Distance/Off-Campus.

Units are offered in attending mode unless otherwise indicated (that is attendance is required at the campus identified). A unit identified as offered by distance, that is there is no requirement for attendance, is identified with a nominal enrolment campus. A unit offered to both attending students and by distance from the same campus is identified as having both modes of study.

Special approval is required for enrolment into TNE Program units.

TNE Program units special approval requirements.

* The Final WW Date is the final date from which you can withdraw from the unit without academic penalty, however you will still incur a financial liability (see withdrawal dates explained for more information).

Unit census dates currently displaying for 2020 are indicative and subject to change. Finalised census dates for 2020 will be available from the 1st October 2020.

About Census Dates



Band CSP Student Contribution Full Fee Paying (domestic) Field of Education
2 2020: $1,190.00 2020: $2,402.00 010101

Fees for next year will be published in October. The fees above only apply for the year shown.

Please note: international students should refer to this page to get an indicative course cost.




Teaching Pattern

3x 1hr lecture per week


End of semester 3-hr exam (70%), Assignments (30%)

TimetableView the lecture timetable | View the full unit timetable



Information about any textbook requirements will be available from mid November.

The University reserves the right to amend or remove courses and unit availabilities, as appropriate.