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DEGREE REGULATIONS & PROGRAMMES OF STUDY 2019/2020

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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Fourier Analysis (MATH10051)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 10 (Year 4 Undergraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
SummaryThis 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.
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: Honours Analysis (MATH10068)
Co-requisites
Prohibited Combinations Other requirements Students might find it useful to have taken, or be taking, MATH10047 Essentials in Analysis and Probability.

Information for Visiting Students
Pre-requisitesNone
High Demand Course? Yes
Course Delivery Information
Academic year 2019/20, 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 95 %, Coursework 5 %, Practical Exam 0 %
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:
  1. Demonstrate facility Fourier series and their coefficients.
  2. Use the main ideas of Fourier Analysis, in both the proof of structural properties and in concrete situations.
  3. Work with theoretical and concrete concepts related to Fourier series and their coefficients.
  4. Produce examples and counterexamples illustrating the mathematical concepts presented in the course.
  5. Understand the statements and proofs of important theorems, and explain the key steps in proofs, sometimes with variation.
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
Course URL https://info.maths.ed.ac.uk/teaching.html
Graduate Attributes and Skills Not entered
KeywordsFAn
Contacts
Course organiserProf A Carbery
Tel: (0131 6)50 5993
Email: A.Carbery@ed.ac.uk
Course secretaryMiss Sarah McDonald
Tel: (0131 6)50 5043
Email: sarah.a.mcdonald@ed.ac.uk
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