MA3CV-Calculus of Variations

Module Provider: Mathematics and Statistics
Number of credits: 10 [5 ECTS credits]
Level:6
Terms in which taught: Spring term module
Pre-requisites: MA2DE Differential Equations or MA2DE2NU Differentiable Equations II
Non-modular pre-requisites:
Co-requisites:
Modules excluded: MA4CV 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.

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 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).Ìý

Formative assessment methods:

Problem sheets.

Penalties for late submission:

The Support Centres will apply the following penalties for work submitted late:

• where the piece of work is submitted after the original deadline (or any formally