Module Identifier | PH27010 | ||

Module Title | CONCEPTS IN PHYSICS 2 | ||

Academic Year | 2000/2001 | ||

Co-ordinator | Dr Geraint Thomas | ||

Semester | Semester 1 | ||

Other staff | Dr Nicholas Mitchell, Dr James Whiteway | ||

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

Course delivery | Lecture | 18 lectures | |

Seminars / Tutorials | 3 workshops; 2 tutorials | ||

Assessment | Exam | End of semester examinations | 70% |

Course work | Examples Sheets Deadlines (by week of semester):
Example Sheets 1, 2 and 4 Weeks 2,3 & 5
Example Sheets 6,7, and 9 Weeks 7,8 & 10
| 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:

- 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.

**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; Concpet of a non-integer dimension

Implications on non-linear behaviour in deterministic systems

**Reading Lists**

**Books**
**** 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 : PH27010