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Unit information: Calculus of Variations in 2018/19

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Unit name Calculus of Variations
Unit code MATH30005
Credit points 10
Level of study H/6
Teaching block(s) Teaching Block 2D (weeks 19 - 24)
Unit director Dr. Tourigny
Open unit status Not open

MATH20101 - Ordinary Differential Equations 2



School/department School of Mathematics
Faculty Faculty of Science


Unit aims

To introduce students to the calculus of variation, and to illustrate its use in the solution of some elementary problems arising in mathematics and in physics.

General Description of the Unit

Calculus of Variations is an important branch of optimisation in which the quantity (the functional) to be minimised depends on infinite-dimensional vectors that may for instance represent curves or surfaces. The subject has deep connections with various fields in the natural sciences, including differential geometry, ordinary and partial differential equations, materials science, mathematical biology, etc. It is one of the oldest and yet one of the most used tools for the investigation of problems involving the concept of "free energy". The aims of this course are (1) to cover the basics of the calculus of variations, including the one-variable case, and (2) to illustrate the theory by considering various applications arising in the natural sciences.

Additional unit information can be found at

Intended learning outcomes

After taking this unit, students will:

  1. know the basic techniques and results of the calculus of variations
  2. be able to apply these techniques to solve some problems arising in other areas of science that can be formulated in terms of the minimisation of some functional.

Teaching details

15 lectures with 4 homeworks

Assessment Details

100% Examination.

Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.

Reading and References

Reading and references are available at