2024/25 Undergraduate Module Catalogue

MATH1300 Dynamics and Motion

10 creditsClass Size: 250

Module manager: Prof. Alastair Rucklidge; Dr. Francesca Scarabel
Email: A.M.Rucklidge@leeds.ac.uk; F.Scarabel@leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2024/25

Pre-requisite qualifications

Grade B in A-level Mathematics or equivalent.

This module is not approved as a discovery module

Module summary

In its broadest sense, dynamics refers to the mathematical modelling of things which change with time. The main focus of this module is that of Newtonian Mechanics, where forces cause accelerations which govern the motion of objects (their dynamics), but the module will also explore other examples and applications. The module builds on the methods of calculus (especially solution of ordinary differential equations) from the “Core Mathematics” module. It will also introduce a simple numerical method which allows equations for dynamics to be solved approximately on computers.

Objectives

This module will introduce students to key models in mathematical dynamics, while integrating elements from Core Mathematics and from Computational Mathematics to show how mathematical skills build on each other.

Learning outcomes
On successful completion of the module students will have demonstrated the following learning outcomes relevant to the subject:

1. use mathematics to model a range of physical systems
2. apply the techniques of solution of ordinary differential equations (ODEs) in practical settings
3. use a change of variables to simplify a problem
4. understand the role of conserved quantities in dynamical systems
5. understand dimensions and the role of dimensional and non-dimensional variables in an ODE
6. understand how a simple numerical method can be used to approximate the solution of a physical problem

Skills Learning Outcomes

SLO1. Solve physical problems using mathematical concepts and numerical methods.
SLO2. Model complex systems in a mathematical framework.
SLO3. Use technology appropriately in your work and studies.
SLO4. Visualise complex phenomena and information.

Syllabus

The following topics will be covered:
1. Units, dimensions and variables
2. Newton's laws of motion and examples
3. Conservation laws: momentum, work, energy, potential, escape velocity
4. Impulses and the delta function
5. Collisions, bouncing and centre of mass frame
6. Oscillatory motion: simple harmonic motion, damping, forced oscillation and resonance, phase plane.
7. Circular motion and angular momentum: orbits and Kepler's laws
8. Examples from related systems, e.g. electrical circuits, charged particles, interacting populations
9. A simple numerical method for initial value problems: Euler’s method and limitations

Methods of Assessment

We are currently refreshing our modules to make sure students have the best possible experience. Full assessment details for this module are not available before the start of the academic year, at which time details of the assessment(s) will be provided.

Assessment for this module will consist of;

1 x Portfolio of assessed questions
1 x In-person open book exam

Teaching methods

Delivery type	Number	Length hours	Student hours
Lectures	22	1.00	22.00
seminars	5	1.00	5.00
Independent online learning hours			24.00
Private study hours			49.00
Total Contact hours			27.00
Total hours (100hr per 10 credits)			100.00

Opportunities for Formative Feedback

Regular example sheets.

Reading list

The reading list is available from the Library website

Last updated: 19/08/2024

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