Module Identifier | PH37010 | ||

Module Title | CONCEPTS IN PHYSICS II | ||

Academic Year | 2001/2002 | ||

Co-ordinator | Dr Geraint Thomas | ||

Semester | Semester 1 | ||

Other staff | Dr Nicholas Mitchell | ||

Pre-Requisite | Physics Level 1 Core Modules | ||

Course delivery | Lecture | 18 lectures | |

Seminars / Tutorials | 2 tutorials | ||

Workshop | 3 workshops | ||

Assessment | 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

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

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

E.G. Steward.

James Gleick.

Abarbanel, Rabinovich and Sushchik.