Undergraduate Course: Fourier Analysis (PHYS09054)
|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
|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.
- 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
Information for Visiting Students
|High Demand Course?
Course Delivery Information
|Academic year 2020/21, Available to all students (SV1)
|Learning and Teaching activities (Further Info)
Lecture Hours 11,
Seminar/Tutorial Hours 11,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
|Assessment (Further Info)
|Additional Information (Assessment)
||Coursework 20%, examination 80%.
||Hours & Minutes
|Main Exam Diet S1 (December)||2:00|
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.
|Graduate Attributes and Skills
|Course organiser||Dr Jorge Penarrubia
Tel: 0131 668 8359
|Course secretary||Miss Helen Walker
Tel: (0131 6)50 7741