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# Numerical Analysis - MAT00094H

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• Department: Mathematics
• Credit value: 20 credits
• Credit level: H
• Academic year of delivery: 2024-25
• See module specification for other years: 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 period
A Semester 2 2024-25

## Module aims

The module aims to provide you with the basic skills needed to make practical use of mathematical descriptions of real-world phenomena, because mathematical equations are almost always solvable only by numerical means. The module also aims to give you the ability to assess the reliability of numerical methods and to adapt the methods to new problems.

## 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 Python to apply the numerical techniques 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.

## Indicative assessment

Closed/in-person Exam (Centrally scheduled) 60
Essay/coursework 40

### Special assessment rules

None

The coursework mark will be made up of 10 smaller pieces of work completed during the semester.

### Indicative reassessment

Closed/in-person Exam (Centrally scheduled) 60
Essay/coursework 40

## 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.