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|
|Faculty/School||College of Sciences and Engineering
School of Natural Sciences
|Discipline||Mathematics & Physics|
|Available as student elective?||Yes|
This unit is currently unavailable.
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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.
|Band||Field of Education|
Fees for next year will be published in October. The fees above only apply for the year shown.
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3x 1hr lecture per week
End of semester 3-hr exam (70%), Assignments (30%)
|Timetable||View the lecture timetable | View the full unit timetable|
Information about any textbook requirements will be available from mid November.
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