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Unit information: Calculus of Variations in 2021/22

Unit name Calculus of Variations
Unit code MATHM0015
Credit points 10
Level of study M/7
Teaching block(s) Teaching Block 1B (weeks 7 - 12)
Unit director Dr. Slastikov
Open unit status Not open
Pre-requisites

MATH20015 Multivariable Calculus and Complex Functions and MATH20101 Ordinary Differential Equations 2

Co-requisites

None

School/department School of Mathematics
Faculty Faculty of Science

Description including Unit Aims

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 Information

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 Information

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.

Resources

If this unit has a Resource List, you will normally find a link to it in the Blackboard area for the unit. Sometimes there will be a separate link for each weekly topic.

If you are unable to access a list through Blackboard, you can also find it via the Resource Lists homepage. Search for the list by the unit name or code (e.g. MATHM0015).

How much time the unit requires
Each credit equates to 10 hours of total student input. For example a 20 credit unit will take you 200 hours of study to complete. Your total learning time is made up of contact time, directed learning tasks, independent learning and assessment activity.

See the Faculty workload statement relating to this unit for more information.

Assessment
The Board of Examiners will consider all cases where students have failed or not completed the assessments required for credit. The Board considers each student's outcomes across all the units which contribute to each year's programme of study. If you have self-certificated your absence from an assessment, you will normally be required to complete it the next time it runs (this is usually in the next assessment period).
The Board of Examiners will take into account any extenuating circumstances and operates within the Regulations and Code of Practice for Taught Programmes.

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