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# Numerical Analysis - MAT00041H

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

## Related modules

• None

### Prohibited combinations

Pre-requisite modules:

Calculus (MAT00001C) and Algebra (MAT0010C), or

Mathematics for the Sciences I (MAT00007C) and Mathematics for the Sciences II (MAT00008C).

Plus Mathematical Skills II (MAT00027I), or sufficient programming skills obtained otherwise (e.g., through the Mathematics and Computer Science Combined programme)

## Module will run

Occurrence Teaching period
A Autumn Term 2022-23 to Spring Term 2022-23

## 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.

• 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
Closed/in-person Exam (Centrally scheduled)
Numerical Analysis
2 hours 60
Coursework - extensions not feasible/practicable
Computer-based assessments
N/A 20
Essay/coursework
AUT written coursework 1
N/A 2.5
Essay/coursework
AUT written coursework 2
N/A 2.5
Essay/coursework
AUT written coursework 3
N/A 2.5
Essay/coursework
AUT written coursework 4
N/A 2.5
Essay/coursework
SPR written coursework 1
N/A 2.5
Essay/coursework
SPR written coursework 2
N/A 2.5
Essay/coursework
SPR written coursework 3
N/A 2.5
Essay/coursework
SPR written coursework 4
N/A 2.5

None

### Reassessment

Task Length % of module mark
Closed/in-person Exam (Centrally scheduled)
Reassessment - closed examination - 3 hrs
3 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.