This module is designed to introduce students to central elements of applied mathematics. It assumes no prior knowledge of particular applications, but assumes a working understanding of basic vector algebra and simple differential equations. The module provides the foundation more advanced applied mathematics as well as an interesting self-contained module for students who do not wish to take other applied mathematics modules subsequently.
The module focuses on Newtonian and relativistic dynamics, two of the great intellectual developments in scientific history. These provide beautiful and accurate descriptions of physical situations from the human to astronomical scales, for bodies travelling at speed up to (near) that of light.
The last part of the module introduces a systematic beautiful mathematical treatment that prepares the way for the user to study the dynamics of more complicated contexts such as general relativity.
Applications include fluid flow, rockets, fairground rides, Halley’s comet, spacecraft, the weather and even doing your laundry!
One of the prerequisites for MATH2044, MATH3006, MATH3072 and MATH6149
Pre-requisites: MATH1048 AND MATH1059
Aims and Objectives
Having successfully completed this module you will be able to:
- understand the fundamental concepts of special relativity
- derive key results for time dilation, length contraction and velocity addition at high speed
- derive and solve the differential equations arising from Newton’s laws of motion applied to simple situations using vector notation
- recall and apply the concept of the Lagrangian in simple situations
- understand and exploit the conservation laws of momentum and energy for simple situations;
- understand the concepts of relative velocity and of gravitational and frictional forces
Revision of vector algebra
General motion: position/velocity/acceleration components
Forces and energy
Time dilation/length contraction
four-momentum and E=mc2
Centre of mass/equilibrium
Simple forces: gravity, friction, elasticity
Conservation of mass, linear momentum
Collisions (including relativistic effects)
Rigid body motion
Cylindrical and spherical polar coordinates
The calculus of variations
The Euler-Lagrange equations
Learning and Teaching
Teaching and learning methods
The lecturer will provide a structured week-by-week study programme, based largely on the notes provided. Each week there will be three hours of lectures. There will be a problems class every week, each lasting one hour which will be used to study problems illustrating the lecture material. Students may also attend a workshop each week to gain additional personal help with understanding lecture material or problem sheets. Students should spend their private study time studying the lecture notes and working through these problem sets. Online learning materials are also provided via the a Blackboard website.
|Practical classes and workshops||6|
|Total study time||150|
Resources & Reading list
Gregory D.R.. Classical Mechanics. CUP.
This is how we’ll formally assess what you have learned in this module.
This is how we’ll assess you if you don’t meet the criteria to pass this module.
Repeat type: Internal & External