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Numerical Analysis - MAT00094H

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• Department: Mathematics
• Module co-ordinator: Dr. Gustav Delius
• Credit value: 20 credits
• Credit level: H
• Academic year of delivery: 2023-24

Module summary

The field of numerical analysis allows for the numerical approximation of solutions of mathematical equations using computational algorithms. This module introduces methods for mathematical problems such as the approximation of roots, derivatives and integrals of a function, and solutions to ODEs and PDEs.

Module will run

Occurrence	Teaching cycle
A	Semester 2 2023-24

Module aims

The field of numerical analysis allows for the numerical approximation of solutions of mathematical equations using computational algorithms. This module introduces methods for mathematical problems such as the approximation of roots, derivatives and integrals of a function, and solutions to ODEs and PDEs.

Module learning outcomes

By the end of this module students will be expected to:

1. Apply an appropriate numerical technique to approximate the solution to various mathematical problems.

2. Mathematically analyse the stability and/or error of a given numerical technique (e.g. the local truncation and total error of a particular integration method or the region of stability for a Runge-Kutta method).

3. Use a computational coding language (such as MATLAB, MAPLE, C++, Python, etc.) to apply a numerical technique learned in the module.

Module content

The module will cover basic numerical techniques used in the vast majority of applications in science and technology. Specifically, methods for (1) root finding (Binomial, Secant, and Newton's methods), (2) calculation of the solution to a system of linear equations such as Ax=b, (3) interpolation of data points using polynomials and splines, (4) numerical approximation of derivatives and integrals, (5) the minimization of functions, and (6) solutions to ODEs and PDEs.

Assessment

Task	Length	% of module mark
Closed/in-person Exam (Centrally scheduled) Closed exam : Numerical Analysis	2 hours	60
Essay/coursework Coursework : Computer and Written Exercises	N/A	4
Essay/coursework Coursework : Computer and Written Exercises	N/A	4
Essay/coursework Coursework : Computer and Written Exercises	N/A	4
Essay/coursework Coursework : Computer and Written Exercises	N/A	4
Essay/coursework Coursework : Computer and Written Exercises	N/A	4
Essay/coursework Coursework : Computer and Written Exercises	N/A	4
Essay/coursework Coursework : Computer and Written Exercises	N/A	4
Essay/coursework Coursework : Computer and Written Exercises	N/A	4
Essay/coursework Coursework : Computer and Written Exercises	N/A	4
Essay/coursework Coursework : Computer and Written Exercises	N/A	4

Special assessment rules

None

Additional assessment information

Exceptional circumstances during term time will be taken into account via extended deadlines on the coursework.

Reassessment

Task	Length	% of module mark
Closed/in-person Exam (Centrally scheduled) Closed exam : Numerical Analysis	N/A	60
Essay/coursework Coursework : Computer and Written Exercises	N/A	4

Module feedback

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

Indicative reading

Burden, Faires “Numerical analysis”

Butcher, “Numerical Methods for ODEs”

Press et al, “Numerical Recipes in C++”