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:
Metric Spaces (MATH10101)
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Co-requisites | |
| Prohibited Combinations | |
Other requirements | A pass in Honours Analysis (MATH10068) in 2020-21 or earlier is an acceptable substitute for a pass in Metric Spaces (MATH10101)
Students might find it useful to have taken MATH10047 Essentials in Analysis and Probability.
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Information for Visiting Students
| Pre-requisites | Visiting students are advised to check that they have studied the material covered in the syllabus of each prerequisite course before enrolling.
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| High Demand Course? |
Yes |
Course Delivery Information
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| Academic year 2022/23, Available to all students (SV1)
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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 )
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| Assessment (Further Info) |
Written Exam
95 %,
Coursework
5 %,
Practical Exam
0 %
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| Additional Information (Assessment) |
Coursework 5%, Examination 95% |
| Feedback |
Not entered |
| Exam Information |
| Exam Diet |
Paper Name |
Hours & Minutes |
|
| Main Exam Diet S2 (April/May) | Fourier Analysis (MATH10051) | 2:00 | |
Learning Outcomes
On completion of this course, the student will be able to:
- Demonstrate facility 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 |
Contacts
| Course organiser | Dr Jonathan Hickman
Tel: (0131 6)50 5060
Email: |
Course secretary | Mrs Alison Fairgrieve
Tel: (0131 6)50 5045
Email: |
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