Undergraduate Course: Fourier Analysis (MATH10051)
|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
|Summary||This is a course in the rigorous treatment of Fourier series and related topics.
- 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.
Entry Requirements (not applicable to Visiting Students)
|| Students MUST have passed:
Honours Analysis (MATH10068)
||Other requirements|| Students might find it useful to have taken, or be taking, MATH10047 Essentials in Analysis and Probability.
In academic year 2022-23 and later, MATH10101 Metric Spaces is a prerequisite for this course.
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 22,
Seminar/Tutorial Hours 5,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
|Assessment (Further Info)
|Additional Information (Assessment)
||Coursework 5%, Examination 95%
||Hours & Minutes
|Main Exam Diet S2 (April/May)||Fourier Analysis (MATH10051)||2:00|
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.
|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
|Course organiser||Prof A Carbery
Tel: (0131 6)50 5993
|Course secretary||Mr Christopher Palmer
Tel: (0131 6)50 5060