Course ObjectiveAt the end of this course the student is able to:
a) Calculate the Fourier series of a given Riemann-integrable function
b) Determine the pointwise and prove the mean-square convergence of a
c) Determine good kernels
d) Apply Fourier series theory to Cesàro and Abel summability
e) Calculate the Fourier transfom on the real line
f) Apply the Fourier transform to some PDE's
Course ContentTopics that will treated are:
a) The genesis of Fourier Analysis, in particular the investigation of
the wave equation
b) Basic Properties of Fourier Series (uniqueness, convolutions,
Dirichlet and Poisson kernels)
c) Convergence of Fourier Series (pointwise, mean-square)
d) Cesàro and Abel Summability
e) Some applications of Fourier Series
f) The Fourier transform on the real line (definition, inversion,
g) Applications of the Fourier transform to some partial differential
Teaching MethodsLectures (1x2 hours per week) and Tutorials (1x2 hours per week).
Active participation during the tutorials is expected!
Method of AssessmentThere are hand-in exercises with grade H, a midterm with grade M and a
final exam with grade F. Let A=.5(M+F) and B=.1 H+.9 A. To pass the
course the student must have A>=.5 and B>=5.5. The final grade is then
B. There is one resit opportunity for the full course. The grade for the
homework does not count toward the grade of resit.
Fourier Analysis, an Introduction, by Elias M. Stein and Rami Shakarchi.
Princeton Lectures in Analysis I. Princeton University Press, 2003,
Target AudienceBachelor Mathematics Year 2
Recommended background knowledgeFirst year courses Single variable calculus, Multivariable calculus,
Linear algebra, and Mathematical analysis.
|Language of Tuition||English|
|Faculty||Faculty of Science|
|Course Coordinator||dr. T.O. Rot|
|Examiner||prof. dr. G.J.B. van den Berg|
dr. T.O. Rot
You need to register for this course yourself
Last-minute registration is available for this course.
|Teaching Methods||Seminar, Lecture|
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