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 20point Fourier Analysis and Statistics course, without the statistics content. Examined via a single twohour 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; SturmLiouville theory: complete basis set of functions

Information for Visiting Students
Prerequisites  None 
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:
100
(
Lecture Hours 11,
Seminar/Tutorial Hours 11,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
76 )

Assessment (Further Info) 
Written Exam
80 %,
Coursework
20 %,
Practical Exam
0 %

Additional Information (Assessment) 
Coursework 20%, examination 80%. 
Feedback 
Not entered 
Exam Information 
Exam Diet 
Paper Name 
Hours & Minutes 

Main Exam Diet S1 (December)   2:00  
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 nonmathematical 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.

Additional Information
Graduate Attributes and Skills 
Not entered 
Keywords  FA 
Contacts
Course organiser  Dr Jorge Penarrubia
Tel: 0131 668 8359
Email: jorpega@roe.ac.uk 
Course secretary  Miss Helen Walker
Tel: (0131 6)50 7741
Email: hwalker7@ed.ac.uk 

