## MA4CV-Calculus of Variations

Module Provider: Mathematics and Statistics
Number of credits: 10 [5 ECTS credits]
Level:7
Terms in which taught: Autumn term module
Pre-requisites: MA2DE Differential Equations or MA2ODE Ordinary Differential Equations and MA2VC Vector Calculus or MA3VC Vector Calculus
Non-modular pre-requisites:
Co-requisites:
Modules excluded: MA3CV Calculus of Variations
Module version for: 2017/8

Module Convenor: Prof Paul Glaister

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.

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 length lying on a surface.

Brief description of teaching and learning methods:

Lectures supported by problem sheets.

Contact hours:
 Autumn Spring Summer Lectures 20 Guided independent study 80 Total hours by term 100.00 Total hours for module 100.00

Summative Assessment Methods:
 Method Percentage Written exam 100

Other information on summative assessment:

Formative assessment methods:

Problem sheets.

Penalties for late submission:
The Module Convenor will apply the following penalties for work submitted late, in accordance with the University policy.

• where the piece of work is submitted up to one calendar week after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for the piece of work will be deducted from the mark for each working day (or part thereof) following the deadline up to a total of five working days;
• where the piece of work is submitted more than five working days after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.

• The University policy statement on penalties for late submission can be found at: http://www.reading.ac.uk/web/FILES/qualitysupport/penaltiesforlatesubmission.pdf
You are strongly advised to ensure that coursework is submitted by the relevant deadline. You should note that it is advisable to submit work in an unfinished state rather than to fail to submit any work.

Length of examination:

2 hours.

Requirements for a pass:

A mark of 50% overall.

Reassessment arrangements:

One examination paper of 2 hours duration in August/September.