Courses & Units

Calculus of Variations KMA381

Note:

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

Introduction

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.

Summary

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 & Physics
Teaching staff

Prof L Forbes

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

Availability

This unit is currently unavailable.

Note

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Unit census dates currently displaying for 2019 are indicative and subject to change. Finalised census dates for 2019 will be available from the 1st October 2018.

About Census Dates

Fees

Domestic

Band Field of Education
2 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.

Requisites

Prerequisites

Teaching

Teaching Pattern

3x 1hr lecture per week

Assessment

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

TimetableView the lecture timetable | View the full unit timetable

Textbooks

Required

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

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