|| PH37010 |
|| CONCEPTS IN PHYSICS II |
|| 2001/2002 |
|| Dr Geraint Thomas |
|| Semester 1 |
|| Dr Nicholas Mitchell |
|| Physics Level 1 Core Modules |
| Course delivery
|| Lecture || 18 lectures |
|| Seminars / Tutorials || 2 tutorials |
|| Workshop || 3 workshops |
|| Course work || Examples sheets Coursework Deadlines to be announced at beginning of module || 30% |
|| Exam || 2 Hours End of semester examinations || 70% |
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.
After taking this module students should be able to:
Understand the concept of Fourier analysis of signals
Understand the concept of Convolution and Correlation
Appreciate the role of Fourier analysis in a number of physical systems
Develop simple models to approximate physical situations
Understand the difference between the evolution of linear and non-linear systems
Appreciate the significance of higher order terms and perturbations on the evolution of physical systems and models
Additional learning activities
Workshops to provide practice in the development of modelling and approximation techniques.
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
** Recommended Text
FOURIER OPTICS an Introduction. Ellis Horwood 0745801862
** Supplementary Text
CHAOS. Heinemann 042429554X
Abarbanel, Rabinovich and Sushchik.
An Introduction to Non-Linear Dynamics for Physicists. World Scientific 9810214103