MA3CVNU-Calculus of Variations

Module Provider: Mathematics and Statistics
Number of credits: 10 [5 ECTS credits]
Level:6
Semesters in which taught: Semester 2 module
Pre-requisites: MA2DE2NU Differentiable Equations II
Non-modular pre-requisites:
Co-requisites:
Modules excluded:
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.

The Module lead at NUIST isÌýDr Tang Xingdong (txd@nuist.edu.cn).

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 length joining 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	Semester 1	Semester 2
Lectures		36
Tutorials		12
Guided independent study:	Ìý	Ìý
Ìý Ìý Wider reading (independent)		10
Ìý Ìý Wider reading (directed)		10
Ìý Ìý Exam revision/preparation		12
Ìý Ìý Advance preparation for classes		10
Ìý Ìý Revision and preparation		10
Ìý	Ìý	Ìý
Total hours by term	0	100
Ìý	Ìý	Ìý
Total hours for module	100

Summative Assessment Methods:

Method	Percentage
Written exam	100

Summative assessment- Examinations:

2 hours

Summative assessment- Coursework and in-class tests:

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.

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