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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)

- Practical Curve fitting and data analysis, least squares line fitting
- Discrete and continuous probabilities; connection to physical processes; 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; power-law processes and distributions
- Hypothesis testing; idea of test statistics; z-test; 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;
- Model fitting;
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: Linear Algebra and Several Variable Calculus (PHYS08042) AND Dynamics and Vector Calculus (PHYS08043) AND ( Experimental Physics 2 (PHYS08056) OR Experimental Physics 2 (PHYS08058))
Co-requisites
Prohibited Combinations Students MUST NOT also be taking Fourier Analysis (PHYS09054)
Other requirements None
Additional Costs None
Information for Visiting Students
Pre-requisitesNone
High Demand Course? Yes
Course Delivery Information
Academic year 2024/25, Available to all students (SV1) Quota:  None
Course Start Semester 1
Timetable Timetable
Learning and Teaching activities (Further Info) Total Hours: 200 ( Lecture Hours 44, Seminar/Tutorial Hours 36, Formative Assessment Hours 3, Programme Level Learning and Teaching Hours 4, Directed Learning and Independent Learning Hours 113 )
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 Dec Exam3:180
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
None
Additional Information
Graduate Attributes and Skills Not entered
KeywordsFASt
Contacts
Course organiserProf Graeme Ackland
Tel: (0131 6)50 5299
Email: gjackland@ed.ac.uk
Course secretaryMs Nicole Ross
Tel:
Email: nicole.ross@ed.ac.uk
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