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Semester 1

Fourier Analysis (PHYS09054)

Subject

Physics and Astronomy

College

SCE

Credits

10

Normal Year Taken

3

Delivery Session Year

2022/2023

Pre-requisites

Course Summary

Half of the 20-point Fourier Analysis and Statistics course, without the statistics content. Examined via a single two-hour paper in the December diet.

Course Description

- Fourier series: sin and cos as a basis set; calculating coefficients; complex basis; convergence, Gibbs phenomenon- Fourier transform: limiting process; uncertainty principle; application to Fraunhofer diffraction- Dirac delta function: Sifting property; Fourier representation- Convolution; Correlations; Parseval's theorem; power spectrum- Sampling; Nyquist theorem; data compression- Solving Ordinary Differential Equations with Fourier methods; driven damped oscillators- Green's functions for 2nd order ODEs; comparison with Fourier methods- Partial Differential Equations: wave equation; diffusion equation; Fourier solution- Partial Differential Equations: solution by separation of variables- PDEs and curvilinear coordinates; Bessel functions; Sturm-Liouville theory: complete basis set of functions

Assessment Information

Written Exam 80%, Coursework 20%, Practical Exam 0%

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