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)
- 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;
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Information for Visiting Students
| Pre-requisites | None |
| 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 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 |
Minutes |
|
| Main Exam Diet S1 (December) | Fourier Analysis and Statistics Dec Exam | 180 | |
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 Graeme Ackland
Tel: (0131 6)50 5299
Email: |
Course secretary | Ms Nicole Ross
Tel:
Email: |
|
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