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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)

Course Outline
SchoolSchool of Physics and Astronomy CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 9 (Year 3 Undergraduate) AvailabilityAvailable to all students
SCQF Credits20 ECTS Credits10
SummaryA 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
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: ( Linear Algebra and Several Variable Calculus (PHYS08042) OR Algebra and Calculus (PHYS08041)) AND Dynamics and Vector Calculus (PHYS08043) AND ( Practical Physics (PHYS08048) OR Experimental Physics 2 (PHYS08056))
Prohibited Combinations Students MUST NOT also be taking Fourier Analysis (PHYS09054)
Other requirements None
Additional Costs None
Information for Visiting Students
High Demand Course? Yes
Course Delivery Information
Academic year 2021/22, 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)3:00
Learning Outcomes
On completion of this course, the student will be able to:
  1. State in precise terms key concepts relating to Fourier analysis and probability & statistics.
  2. Master the derivations of a set of important results in Fourier analysis and probability & statistics.
  3. Apply standard methods of Fourier analysis and probability & statistics to solve unseen problems of moderate complexity.
  4. 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.
  5. Be able to think critically about the results of solving such problems: whether they make sense physically, and whether different mathematical approaches are equivalent.
Reading List
Additional Information
Graduate Attributes and Skills Not entered
Course organiserDr Jorge Penarrubia
Tel: 0131 668 8359
Course secretaryMiss Helen Walker
Tel: (0131 6)50 7741
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