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Course module: NWI-WB049B
NWI-WB049B
Introduction to Fourier Theory
Course infoSchedule
Course moduleNWI-WB049B
Credits (ECTS)3
CategoryBA (Bachelor)
Language of instructionEnglish
Offered byRadboud University; Faculty of Science; Wiskunde, Natuur- en Sterrenkunde;
Lecturer(s)
Contactperson for the course
dr. A.Y. Burtscher
Other course modules lecturer
Examiner
dr. A.Y. Burtscher
Other course modules lecturer
Cursuscoördinator
dr. A.Y. Burtscher
Other course modules lecturer
Lecturer
dr. A.Y. Burtscher
Other course modules lecturer
Academic year2019
Period
KW3  (03/02/2020 to 12/04/2020)
Starting block
KW3
Course mode
full-time
Remarks-
Registration using OSIRISYes
Course open to students from other facultiesYes
Pre-registrationNo
Waiting listNo
Placement procedure-
Aims
  • The student is familiar with the fundaments of the theory of Fourier series, of the Fourier transform, and of the finite Fourier theory.
  • The student knows the most important theorems, like the inversion theorem, the Parseval/Plancherel formula and Poisson summation.
  • The student is able to recognize situations where the theory applies and can use it for solution of a broad class of partial differential equations.
  • The student has some understanding of the connection between Fourier theory and character theory of abelian groups.
Content
This course is based on a recent book by Elias Stein, one of the best known exports in the field of Fourier analysis, also known as harmonic analysis. Fourier analysis begins with the idea of Fourier that "every" periodic function is an (infinite) linear combination of sine and cosine functions, but quite some work is required in order to make this idea precise. These Fourier series, as well as the Fourier transform, have many applications to (partial) differential equations and even to number theory! We will also have a look at Fourier theory on finite abelian groups (which in principle is part of algebra), which has many important applications.
Test information
Written exam
Prerequisites
Analysis 1 + 2 (possibly also students of physics that have followed Calculus A and B).
Required materials
Book
Elias M. Stein & Rami Shakarchi: Fourier Analysis. An Introduction (Part I of the Princeton Lectures in Analysis) Princeton University Press, Princeton 2003.
Instructional modes
Course occurrence

Lecture

Tutorial

Zelfstudie

Tests
Exam
Test weight1
Test typeExam
OpportunitiesBlock KW3, Block KW4

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