Undergraduate Course: Fourier Analysis and Statistics (PHYS09055)
Course Outline
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
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Information for Visiting Students
Pre-requisites | None |
High Demand Course? |
Yes |
Course Delivery Information
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Academic year 2015/16, Available to all students (SV1)
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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 )
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Assessment (Further Info) |
Written Exam
80 %,
Coursework
20 %,
Practical Exam
0 %
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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 | | Main Exam Diet S1 (December)Main Exam Diet S2 (April/May)Resit Exam Diet (August)Outwith Standard Exam Diets JanuaryOutwith Standard Exam Diets FebruaryOutwith Standard Exam Diets MarchOutwith Standard Exam Diets AprilOutwith Standard Exam Diets MayOutwith Standard Exam Diets JuneOutwith Standard Exam Diets JulyOutwith Standard Exam Diets AugustOutwith Standard Exam Diets SeptemberOutwith Standard Exam Diets OctoberOutwith Standard Exam Diets NovemberOutwith Standard Exam Diets DecemberResit Exam Diet (April/May Sem 1 resits only) | Temp exam | : | |
Learning Outcomes
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.
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Additional Information
Graduate Attributes and Skills |
Not entered |
Keywords | FASt |
Contacts
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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© Copyright 2015 The University of Edinburgh - 2 September 2015 4:43 am
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