Module Identifier PH37010  
Academic Year 2000/2001  
Co-ordinator Dr Geraint Thomas  
Semester Semester 1  
Other staff Dr Nicholas Mitchell, Dr James Whiteway  
Pre-Requisite Physics Level 1 Core Modules  
Course delivery Lecture   18 lectures  
  Seminars / Tutorials   2 tutorials  
  Workshop   3 workshops  
Assessment Exam   End of semester examinations   70%  
  Course work   Examples sheets Coursework Deadlines to be announced at beginning of module   30%  

Module description
This module introduces a number of concepts which are fundamental in all branches of Physics. The representation of a data series in terms of complementary parameters (such as time and frequency, or distance and angle) is used to introduce Fourier theory and the relationship between a function and its Fourier transform, autocorrelation function and power spectrum.

The difference between linear and non-linear equations is demonstrated, including the generation of sum and difference frequencies in non-linear processing. The use of dimensionless numbers in solving non-linear equations is illustrated and the relationship between non-linear equations and chaos theory is explored through solutions of the difference equation.

Finally, modelling techniques are introduced and examples of applications to specific problems are presented.

Learning outcomes
After taking this module students should be able to:

Additional learning activities
Workshops to provide practice in the development of modelling and approximation techniques.

Outline syllabus
Fourier series
Fourier transforms
Convolution and correlations

Introduction to the concepts and philosophy of modelling
Development of models as a problem solving tool in physics.

Simple pendulum as a linear oscillator
The concept of phase space
Trajectories in phase space: periodic and non-periodic behaviour; deterministic chaos
Modelling the atmosphere and the Lorentz attractor
Non-linear electrical circuit
Logistic difference equation
Bifurcation and period doubling, the Feigenbaum number
Relationship between Chaos and Fractals; Concept of a non-integer dimension
Implications on non-linear behaviour in deterministic systems

Reading Lists
** Recommended Text
E.G. Steward. FOURIER OPTICS an Introduction. Ellis Horwood
** Supplementary Text
James Gleick. CHAOS. Heinemann
Abarbanel, Rabinovich and Sushchik. An Introduction to Non-Linear Dynamics for Physicists. World Scientific Lecture Notes in Physics Invalid isbn : 981021410 : An Introduction to Non-Linear Dynamics for Physicists : PH37010