Undergraduate Course: Fourier Analysis (MATH10051)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 10 (Year 4 Undergraduate) |
Availability | Available to all students |
| SCQF Credits | 10 |
ECTS Credits | 5 |
| Summary | This is a course in the rigorous treatment of Fourier series and related topics. |
| Course description |
- Fourier series, Fourier coefficients, trigonometric polynomials and orthogonality.
- Properties of Fourier coefficients; Bessel's inequality, Parseval's identity and the Riemann-Lebesgue lemma.
- Various notions of convergence of Fourier series, including pointwise, uniform and mean square convergence. Summability methods, convolution and Young's inequality.
- Fourier Analysis in broader contexts; for example, Fourier integrals, Fourier expansions in groups, Schwartz spaces and tempered distributions.
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Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
Students MUST have passed:
Honours Analysis (MATH10068)
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Co-requisites | |
| Prohibited Combinations | |
Other requirements | Students might find it useful to have taken MATH10047 Essentials in Analysis and Probability.
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Information for Visiting Students
| Pre-requisites | This is a Year 4, Honours level course. Visiting students are expected to have an academic profile equivalent to the first three years of the BSc (Hons) Mathematics programme (UTMATHB). Students should have passed courses equivalent to Honours Analysis (MATH10068). Students may also find it beneficial to have passed a course equivalent to Essentials in Analysis and Probability (MATH10047).
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| High Demand Course? |
Yes |
Course Delivery Information
|
| Academic year 2025/26, Available to all students (SV1)
|
Quota: None |
| Course Start |
Semester 2 |
Timetable |
Timetable |
| Learning and Teaching activities (Further Info) |
Total Hours:
100
(
Lecture Hours 22,
Seminar/Tutorial Hours 5,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
69 )
|
| 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 |
Minutes |
|
| Main Exam Diet S2 (April/May) | Fourier Analysis (MATH10051) | 120 | |
Learning Outcomes
On completion of this course, the student will be able to:
- Demonstrate facility with Fourier series and their coefficients.
- Use the main ideas of Fourier Analysis, in both the proof of structural properties and in concrete situations.
- Work with theoretical and concrete concepts related to Fourier series and their coefficients.
- Produce examples and counterexamples illustrating the mathematical concepts presented in the course.
- Understand the statements and proofs of important theorems, and explain the key steps in proofs, sometimes with variation.
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Reading List
1. Fourier Analysis: An Introduction, by E.M. Stein and R. Shakarchi, Princeton University Press.
2. Fourier Series and Integrals, by H. Dym and H. McKean, Academic Press.
3. Fourier Analysis, by T.W. Korner, Cambridge University Press |
Additional Information
| Graduate Attributes and Skills |
Not entered |
| Keywords | FAn |
Contacts
| Course organiser | Dr Jonathan Hickman
Tel: (0131 6)50 5060
Email: Jonathan.Hickman@ed.ac.uk |
Course secretary | Mrs Alison Fairgrieve
Tel: (0131 6)50 5045
Email: Alison.Fairgrieve@ed.ac.uk |
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