# DEGREE REGULATIONS & PROGRAMMES OF STUDY 2015/2016

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

# Undergraduate Course: Fourier Analysis and Statistics (PHYS09055)

 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 20 ECTS Credits 10 Summary A coherent 20pt course taken by all single honours physics students. Examined via a single three-hour paper in the December diet. Course description Fourier Analysis (20 lectures) - 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 Probability and Statistics (20 lectures) - Concept and origin of randomness; randomness as frequency and as degree of belief - Discrete and continuous probabilities; combining probabilities; Bayes theorem - Probability distributions and how they are characterised; moments and expectations; error analysis - Permutations, combinations, and partitions; Binomial distribution; Poisson distribution - The Normal or Gaussian distribution and its physical origin; convolution of probability distributions; Gaussian as a limiting form - Shot noise and waiting time distributions; resonance and the Lorentzian; growth and competition and power-law distributions - Hypothesis testing; idea of test statistics; chi-squared statistic; F-statistic - Parameter estimation; properties of estimators; maximum likelihood methods; weighted mean and variance; minimum chi-squared method; confidence intervals - Bayesian inference; priors and posteriors; maximum credibility method; credibility intervals - Correlation and covariance; tests of correlation; rank correlation test; least squares line fitting - Model fitting; analytic curve fitting; numerical model fitting; methods for finding minimum chi-squared or maximum credibility; multi-parameter confidence intervals; interesting and uninteresting parameters
 Pre-requisites Students MUST have passed: ( Linear Algebra and Several Variable Calculus (PHYS08042) AND Dynamics and Vector Calculus (PHYS08043) AND Practical Physics (PHYS08048)) AND Algebra and Calculus (PHYS08041) Co-requisites Prohibited Combinations Students MUST NOT also be taking Fourier Analysis (PHYS09054) Other requirements None Additional Costs None
 Pre-requisites None High Demand Course? Yes
 Academic year 2015/16, Available to all students (SV1) Quota:  None Course Start Semester 1 Timetable Timetable Learning and Teaching activities (Further Info) Total Hours: 200 ( Lecture Hours 22, Seminar/Tutorial Hours 22, Formative Assessment Hours 3, Programme Level Learning and Teaching Hours 4, Directed Learning and Independent Learning Hours 149 ) Assessment (Further Info) Written Exam 80 %, Coursework 20 %, Practical Exam 0 % Additional Information (Assessment) Coursework 20% and examination 80%. Feedback Not entered Exam Information Exam Diet Paper Name Hours & Minutes Main Exam Diet S1 (December) Fourier Analysis and Statistics 3:00 Academic year 2015/16, Part-year visiting students only (VV1) Quota:  None Course Start Semester 1 Timetable Timetable Learning and Teaching activities (Further Info) Total Hours: 200 ( Lecture Hours 22, Seminar/Tutorial Hours 22, Formative Assessment Hours 3, Programme Level Learning and Teaching Hours 4, Directed Learning and Independent Learning Hours 149 ) Assessment (Further Info) Written Exam 80 %, Coursework 0 %, Practical Exam 20 % Additional Information (Assessment) Coursework 20% and examination 80%. Feedback Not entered Exam Information Exam Diet Paper Name Hours & Minutes Main Exam Diet S1 (December) Fourier Analysis and Statistics 3:00
 On completion of this course, the student will be able to: State in precise terms key concepts relating to Fourier analysis and probability & statistics.Master the derivations of a set of important results in Fourier analysis and probability & statistics.Apply standard methods of Fourier analysis and probability & statistics 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 FASt
 Course organiser Prof John Peacock Tel: (0131) 668 8390 Email: John.Peacock@ed.ac.uk Course secretary Mrs Siobhan Macinnes Tel: (0131 6)51 3448 Email: Siobhan.MacInnes@ed.ac.uk
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