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Numerical Analysis (MSc) - MAT00069H

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• Department: Mathematics
• Module co-ordinator: Dr. Eric Dykeman
• Credit value: 20 credits
• Credit level: H
• Academic year of delivery: 2021-22
  • See module specification for other years: 2022-23

Module summary

This module is for postgraduate students only.

Related modules

Additional information

Pre-requisite:

• Students should have taken an introduction to programming

Module will run

Occurrence	Teaching period
A	Autumn Term 2021-22 to Spring Term 2021-22

Module aims

• To introduce numerical approximation techniques for solving standard problems in Mathematics, and explain when and why they work.
• To derive some of these techniques rigorously from first principles.
• To explain how (packaged) computer software is able to produce numerical solutions, and to enable a judgement of whether the results are reliable.
• To provide opportunities for implementing numerical techniques on a computer.

Module learning outcomes

Subject content

• Derive elementary numerical methods from first principles.
• Apply the numerical methods discussed to simple examples, using pen and paper (i.e., without the help of a computer).
• Implement numerical methods using computer software, and apply them in examples.
• Compute error estimates for simple numerical methods.
• Judge under which circumstances a given numerical method is reliable.

Academic and graduate skills

• Understand some elements of computer programming
• Understand the concept of computer algorithms

Module content

Syllabus

• Numerical errors
• Root finding for functions of one variable
• Root finding for functions of several variables
• Solving linear equation systems
• Interpolation by polynomials
• Numerical integration
• Numerical differentiation
• Initial value problems for ordinary differential equations
• Boundary value problems for ordinary differential equations
• Partial differential equations

Assessment

Task	Length	% of module mark
Online Exam -less than 24hrs (Centrally scheduled) Numerical Analysis	2 hours	100

Special assessment rules

Pass/fail

Additional assessment information

20% of the final exam comes from computer based assessments, and 20% of the final exam comes from written coursework.

Reassessment

Task	Length	% of module mark
Online Exam -less than 24hrs (Centrally scheduled) Numerical Analysis	2 hours	100

Module feedback

Current Department policy on feedback is available in the undergraduate student handbook. Coursework and examinations will be marked and returned in accordance with this policy.

Indicative reading

R L Burden and J D Faires, Numerical Analysis, Brooks/Cole