Module Identifier PH27010 Module Title CONCEPTS IN PHYSICS 2 Academic Year 2001/2002 Co-ordinator Dr Geraint Thomas Semester Semester 1 Other staff Dr Nicholas Mitchell Pre-Requisite Core Physics Modules at Level 1 Course delivery Lecture 18 lectures Seminars / Tutorials 3 workshops; 2 tutorials Assessment Course work Examples Sheets Example Sheets 1,2,4,6,7, & 9 Deadlines are detailed in the Year 2 Example Sheet System distributed by the Department 30% Exam 2 Hours End of semester examinations 70%

#### 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

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