# Gwybodaeth Modiwlau

Module Identifier
PH36010
Module Title
Numerical Methods
2018/2019
Co-ordinator
Semester
Semester 1
Co-Requisite
None.
Pre-Requisite
PH24010 or approval by Degree Scheme co-ordinator
Other Staff

#### Course Delivery

Delivery Type Delivery length / details
Lecture 11 x 1 Hour Lectures
Practical 11 x 2 Hour Practicals

#### Assessment

Assessment Type Assessment length / details Proportion
Semester Assessment Written Report  50%
Semester Assessment Numerical Exercises  30%
Semester Assessment Introductory Exercises  20%
Supplementary Assessment As determined by the Departmental Exam Board.  100%

### Learning Outcomes

On successful completion of this module students should be able to:

1. Utilise various techniques for scientific computing and analysis.
2. Evaluate a range of numerical methods through a series of coding exercises.
3. Compose simple numerical codes for specific techniques in applied physics such as linear interpolation, numerical integration and root finding.
4. Apply numerical codes to solve problems involving Ordinary Differential Equations.
5. Compose a report discussing the application of a numerical method to solve a problem in physics.

### Aims

Computational physics provides an alternative approach to the solution of practical and theoretical problems. Problems that are intractable by analytical techniques can be solved numerically. Numerical simulation is now an important part of physics and other scientific disciplines. Familiarity with numerical techniques and increased computer power provide opportunities for study across the entire range of science and technology, and this module aims to provide an introduction to computational physics by introducing the basic techniques of numerical analysis.

### Brief description

In this course the basic techniques of numerical analysis will be introduced through use of a script-based programming language. Once the basics are introduced, simple methods, such as interpolation, integration and finding the roots of functions will be explored. As the module progresses, more complicated methods such as Fourier transforms are introduced. An important part of the module is the solution of ordinary differential equations which will also form part of the numerical project report.

### Content

This module will comprise a series of 10 lectures with associated 2 hour practical laboratory sessions. After discussing programming techniques, numerical methods will be introduced by reference to the appropriate topics in Physics and will include:

• Linear Interpolation;
• Numerical Integration;
• Root finding;
• Fourier Analysis; and
• Solutions to ordinary differential equations.
Assignments based on the weekly worksheets will be assessed. In addition a small mini project that will comprise the application of a numerical method to a specific physical problem will be completed and assessed.

### Module Skills

Skills Type Skills details
Application of Number Throughout the module.
Communication Writing reports.
Improving own Learning and Performance Students will be expected to develop their own approach to time-management in their attitude to the completion of work on time.
Information Technology This module involves programming and computational visualisation
Personal Development and Career planning Completion of exercises and project to set deadlines will aid personal development.
Problem solving Throughout the module.
Research skills Students will be expected to use the written resources to find supplementary material.
Subject Specific Skills Numerical analysis is a key skill for physics and the physical sciences.
Team work Students will be encouraged to work together on questions during the exercise classes.

### Notes

This module is at CQFW Level 6