MA4CV-Calculus of Variations

Module Provider: Mathematics and Statistics
Number of credits: 10 [5 ECTS credits]
Level:7
Terms in which taught: Spring term module
Pre-requisites:
Non-modular pre-requisites:
Co-requisites:
Modules excluded: MA3CV Calculus of Variations
Current from: 2021/2

Module Convenor: Dr Calvin Smith
Email: Calvin.Smith@reading.ac.uk

Type of module:

Summary module description:

Calculus of variations considers the notion of optimising an integral where the quantity to be varied is a function.

Aims:

• To introduce the notion of optimising a functional in the form of an integral via the classical calculus of variations;


• To place the development of the calculus of variations in an historical setting using appropriate problems and consider techniques for solving such problems.

Assessable learning outcomes:

By the end of the module students are expected to be able to:

• solve problems involving smooth extrema of functionals in the form of an integral.

This module will be assessed to a greater depth than the excluded module MA3CV.

Additional outcomes:

Outline content:

Calculus of variations considers the notion of optimising an integral where the quantity to be varied is a function. This allows us to tackle such problems as finding a curve of minimum lengthÌýjoining two points, or the trajectory which minimises the time taken to move between two points.

Brief description of teaching and learning methods:

Lectures supported by problem sheets.

Summative assessment- Examinations:

2 hours.

Summative assessment- Coursework and in-class tests:

Two set exercises for this module (each worth 10% of the module).

Formative assessment methods:

Problem sheets.

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