Undergraduate Course: Fourier Analysis (PHYS09054)
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 | 10 |
ECTS Credits | 5 |
Summary | Half of the 20-point Fourier Analysis and Statistics course, without the statistics content. Examined via a single two-hour paper in the December diet. |
Course description |
- 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
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Information for Visiting Students
Pre-requisites | None |
High Demand Course? |
Yes |
Course Delivery Information
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Academic year 2024/25, 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:
100
(
Lecture Hours 22,
Seminar/Tutorial Hours 22,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
54 )
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Assessment (Further Info) |
Written Exam
80 %,
Coursework
20 %,
Practical Exam
0 %
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Additional Information (Assessment) |
Coursework 20%, examination 80%. |
Feedback |
Not entered |
Exam Information |
Exam Diet |
Paper Name |
Hours & Minutes |
|
Main Exam Diet S1 (December) | Fourier Analysis Dec Exam | 2:120 | |
Learning Outcomes
On completion of this course, the student will be able to:
- State in precise terms key concepts relating to Fourier analysis.
- Master the derivations of a set of important results in Fourier analysis.
- Apply standard methods of Fourier analysis 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 | FA |
Contacts
Course organiser | Prof Graeme Ackland
Tel: (0131 6)50 5299
Email: gjackland@ed.ac.uk |
Course secretary | Ms Nicole Ross
Tel:
Email: nicole.ross@ed.ac.uk |
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