Undergraduate Course: Fourier Analysis (MATH10051)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Course type | Standard |
Availability | Available to all students |
| Credit level (Normal year taken) | SCQF Level 10 (Year 4 Undergraduate) |
Credits | 10 |
| Home subject area | Mathematics |
Other subject area | None |
| Course website |
https://info.maths.ed.ac.uk/teaching.html |
Taught in Gaelic? | No |
| Course description | This is a course in the rigorous treatment of Fourier series and related topics. |
Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
Students MUST have passed:
Honours Analysis (MATH10068)
|
Co-requisites | |
| Prohibited Combinations | Students MUST NOT also be taking
Linear and Fourier Analysis (MATH10081)
|
Other requirements | Students might find it useful to have taken, or be taking, MATH10047 Essentials in Analysis and Probability.
Students wishing to take both MATH10082 Linear Analysis and MATH10051 Fourier Analysis in the same academic session should register for the 20 credit course MATH10081 Linear and Fourier Analysis. |
| Additional Costs | None |
Information for Visiting Students
| Pre-requisites | None |
| Displayed in Visiting Students Prospectus? | Yes |
Course Delivery Information
|
| Delivery period: 2014/15 Semester 2, Available to all students (SV1)
|
Learn enabled: Yes |
Quota: None |
|
Web Timetable |
Web Timetable |
| Course Start Date |
12/01/2015 |
| Breakdown of 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 )
|
| Additional Notes |
|
| Breakdown of Assessment Methods (Further Info) |
Written Exam
95 %,
Coursework
5 %,
Practical Exam
0 %
|
| Exam Information |
| Exam Diet |
Paper Name |
Hours & Minutes |
|
| Main Exam Diet S2 (April/May) | Fourier Analysis (MATH10051) | 2:00 | |
Summary of Intended Learning Outcomes
1. Facility with Fourier series and their coefficients.
2. Ability to use the main ideas of Fourier Analysis, in both the proof of structural properties and in concrete situations.
3. Capacity to work with theoretical and concrete concepts related to Fourier series and their coefficients.
4. Be able to produce examples and counterexamples illustrating the mathematical concepts presented in the course.
5. Understand the statements and proofs of important theorems and be able to explain the key steps in proofs, sometimes with variation. |
Assessment Information
| Coursework 5%, Examination 95% |
Special Arrangements
| None |
Additional Information
| Academic description |
Not entered |
| Syllabus |
- 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. |
| Transferable skills |
Not entered |
| 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 |
| Study Abroad |
Not entered |
| Study Pattern |
Not entered |
| Keywords | FAn |
Contacts
| Course organiser | Dr Thomas Leinster
Tel: (0131 6)50 5057
Email: Tom.Leinster@ed.ac.uk |
Course secretary | Mrs Alison Fairgrieve
Tel: (0131 6)50 5045
Email: Alison.Fairgrieve@ed.ac.uk |
|
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|
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