PH26020 - THEORETICAL PHYSICS AND CONCEPTS

Module Identifier	PH26020
Module Title	THEORETICAL PHYSICS AND CONCEPTS
Academic Year	2002/2003
Co-ordinator	Dr Andrew Evans
Semester	Semester 1
Other staff	Dr Geraint O Thomas, Dr James A Whiteway
Pre-Requisite	Core Physics at Part 1
Co-Requisite	None
Mutually Exclusive	None
Course delivery	Lecture	30 Hours
	Seminars / Tutorials	4 Workshops
Assessment	Semester Exam	2 Hours	70%
	Semester Assessment	(Example Sheets 1, 2, 3, 4, 5, 6, 7, 8,)	30%

Learning outcomes

Express common physical systems and relationships using the mathematical language of vectors, differential equations,
Fourier theory and modelling
Use vectors and vector algebra to solve physical problems in 3-dimensional space and using different co-ordinate systems
Use different methods of solution for the various types of differential equations and solve simple eigenvalue problems in the physical sciences
Understand the concepts of Fourier analysis, convolution and correlation and appreciate the role of Fourier analysis in 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

Brief description

Building on Year 1 modules on Theoretical Physics 1 (PH) and on Concepts in Physics 1 (PH), this Year 2 20 credit module develops the theoretical background required by all physics students. A wide variety of problems in Physics can be described and analysed in terms of vector operators, differential equations, Fourier analysis and non-linear systems. By the end of the module the student should be able to express common physical systems and relationships using this mathematical language. Topics covered include scalar and vector triple products, polar co-ordinates, 3-D scalar and vector fields, gradient, divergence and curl of 3-D fields, eigenvalue problems, general order ordinary differential equations, simultaneous differential equations, partial differential equations, Fourier analysis of signals, complementary parameters (e.g. frequency and time), Fourier transforms, power spectra, non-linear equations, chaos theory, modelling techniques. The relevance of the above topics to the physical sciences is illustrated throughout with examples drawn from electrostatics, magnetism, gravitation, mechanics, thermo-dynamics. plasma physics, atmospheric physics and fluid dynamics

Reading Lists

Books
** Supplementary Text
M.L Boas. Mathematical Methods in the Physical Sciences. Wiley
** Essential Reading
G.B. Arfken and H.J. Weber. Mathematical Methods for Physicists. 5th. Harcourt
** Recommended Consultation
J. Gleick. Chaos. Abacus ISBN 043429554X
** Supplementary Text
Abarbanel, RAbinovich and Sushchik. An Introduction to Non-Linear Dynamics for Physicists. World Scientific Lecture Notes in Physics 9810214103