## MA2NA1-Numerical Analysis I

Module Provider: Mathematics and Statistics
Number of credits: 10 [5 ECTS credits]
Level:5
Terms in which taught: Spring / Summer term module
Pre-requisites: MA1CA Calculus MA1LA Linear Algebra
Non-modular pre-requisites:
Co-requisites: MA2DE Differential Equations
Modules excluded:
Module version for: 2016/7

Module Convenor: Dr Peter Chamberlain

Summary module description:
This module covers numerical methods in mathematics.

Aims:
To motivate, describe and analyse methods for solving non-linear equations, methods for polynomial interpolation, methods for approximating integrals and methods for approximating solutions to simple differential equations; to develop skills in programming numerical methods (for example, in MATLAB or Python).

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

• Analyse and apply iterative methods for non-linear equations to approximate problems;
• Formulate methods for polynomial interpolation and 'best-fit';
• Formulate and implement methods for approximating integrals;
* Formulate methods for solving simple initial value problems;
• Write computer programs to implement numerical methods.

Outline content:
This module discusses techniques for the solution of non-linear equations. Methods for polynomial interpolation and 'best-fit' curves are considered and methods for approximating integrals are developed. Finally methods are introduced for approximating solutions to certain differential equations.

Brief description of teaching and learning methods:
Lectures supported by problem sheets and practical classes.

Contact hours:
 Autumn Spring Summer Lectures 20 2 Practicals classes and workshops 10 Guided independent study 68 Total hours by term 98.00 2.00 Total hours for module 100.00

Summative Assessment Methods:
 Method Percentage Written exam 70 Set exercise 30

Other information on summative assessment:
Three pieces of assessed work and one examination.

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 40% overall.

Reassessment arrangements:
One examination paper of 2 hours duration in August/September - the resit module mark will be the higher of the exam mark (100% exam) and the exam mark plus previous coursework marks (70% exam, 30% coursework).