# DEGREE REGULATIONS & PROGRAMMES OF STUDY 2017/2018

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DRPS : Course Catalogue : School of Physics and Astronomy : Undergraduate (School of Physics and Astronomy)

# Undergraduate Course: Fourier Analysis (PHYS09054)

 School School of Physics and Astronomy College College of Science and Engineering Credit level (Normal year taken) SCQF Level 9 (Year 3 Undergraduate) Availability Available to all students SCQF Credits 10 ECTS Credits 5 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
 Pre-requisites Students MUST have passed: ( Linear Algebra and Several Variable Calculus (PHYS08042) OR Algebra and Calculus (PHYS08041)) AND Dynamics and Vector Calculus (PHYS08043) Co-requisites Prohibited Combinations Students MUST NOT also be taking Fourier Analysis and Statistics (PHYS09055) Other requirements None
 Pre-requisites None High Demand Course? Yes
 Academic year 2017/18, Available to all students (SV1) Quota:  None Course Start Semester 1 Timetable Timetable Learning and Teaching activities (Further Info) Total Hours: 100 ( Lecture Hours 11, Seminar/Tutorial Hours 11, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 76 ) Assessment (Further Info) Written Exam 80 %, Coursework 20 %, Practical Exam 0 % Additional Information (Assessment) Coursework 20%, examination 80%. Feedback Not entered Exam Information Exam Diet Paper Name Hours & Minutes Main Exam Diet S1 (December) Fourier Analysis (PHYS09054) 2:00
 On completion of this course, the student will be able to: State in precise terms key concepts relating to Fourier analysis.Master the derivations of a set of important results in Fourier analysis.Apply standard methods of Fourier analysis to solve unseen problems of moderate complexity.Understand how to take a physical problem stated in non-mathematical terms and express it in a way suitable for applying the tools of this course.Be able to think critically about the results of solving such problems: whether they make sense physically, and whether different mathematical approaches are equivalent.
 None
 Graduate Attributes and Skills Not entered Keywords FA
 Course organiser Dr Jorge Penarrubia Tel: 0131 668 8359 Email: jorpega@roe.ac.uk Course secretary Miss Yolanda Zapata-Perez Tel: (0131 6)51 7067 Email: yolanda.zapata@ed.ac.uk
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