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
Non-modular pre-requisites:
Co-requisites:
Modules excluded: MA4CV Calculus of Variations
Current from: 2022/3

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.

Contact hours:

Ìý	Autumn	Spring	Summer
Lectures		20
Tutorials		10
Guided independent study:		70
Ìý	Ìý	Ìý	Ìý
Total hours by term	0	100	0
Ìý	Ìý	Ìý	Ìý
Total hours for module	100

Summative Assessment Methods:

Method	Percentage
Written exam	80
Set exercise	20

Summative assessment- Examinations:

2 hours.

The examination for this module will require a narrowly defined time window and is likely to be held in a dedicated exam venue.

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 agreed extension to the deadline): 10% of the total marks available for that 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: /cqsd/-/media/project/functions/cqsd/documents/cqsd-old-site-documents/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.

Assessment requirements for a pass:
A mark of 40% overall.

Reassessment arrangements:

One examination paper of 2 hours duration in August/September.Ìý - the resit module mark will be the higher of the exam mark (100% exam) and the exam mark plus previous coursework marks (80% exam, 20% coursework).

Additional Costs (specified where applicable):

1) Required text books:Ìý

2) Specialist equipment or materials:Ìý

3) Specialist clothing, footwear or headgear:Ìý

4) Printing and binding:Ìý

5) Computers and devices with a particular specification:Ìý

6) Travel, accommodation and subsistence:Ìý

Last updated: 22 September 2022