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Unit information: Calculus of Variations in 2020/21

Unit name Calculus of Variations
Unit code MATHM0015
Credit points 10
Level of study M/7
Teaching block(s) Teaching Block 2D (weeks 19 - 24)
Unit director Dr. Tourigny
Open unit status Not open

MATH20901 Multivariable Calculus and MATH20101 Ordinary Differential Equations 2



School/department School of Mathematics
Faculty Faculty of Science


Unit Aims

To introduce students to calculus of variations and use it to solve basic problems arising in physics, mathematics and materials science.

Unit Description

Calculus of Variations is an important branch of optimization that deals with finding extrema of the functionals in certain functional spaces. It has deep relation with various fields in 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 investigation of the problems involving free energy. The aim of this course is to present the basics of the calculus of variations, including 1D theory and its application to various problems arising in natural sciences.

Intended learning outcomes

After taking this unit, students will:

  1. Understand the basics of the calculus of variations
  2. Will be able to analyze and solve various variational problems arising in physics.

Teaching details

The unit will be taught through a combination of

  • synchronous online and, if subsequently possible, face-to-face lectures
  • asynchronous online materials, including narrated presentations and worked examples
  • guided asynchronous independent activities such as problem sheets and/or other exercises
  • synchronous weekly group problem/example classes, workshops and/or tutorials
  • synchronous weekly group tutorials
  • synchronous weekly office hours

Assessment Details

100% Timed, open-book 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


  • I.M. Gel'fand and S.V. Fomin, Calculus of Variations, Prentice-Hall, 2000
  • Bruce Van Brunt, The Calculus of Variations, Dover, 2010