https://studiegids.vu.nl/en/courses/2024-2025/XB_0005At 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 Fourier series c) Determine good kernels d) Apply Fourier series theory to Cesàro and Abel summability e) Calculate the Fourier transform on the real line f) Apply the Fourier transform to some PDE'sTopics that will treated are: a) Uniform convergence b) The genesis of Fourier Analysis, in particular the investigation of the wave equation c) Basic Properties of Fourier Series (uniqueness, convolutions, Dirichlet and Poisson kernels) d) 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, Plancherel formula) g) Applications of the Fourier transform to some partial differential equationsLectures (1x2 hours per week) and Tutorials (1x2 hours per week). Active participation during the tutorials is expected!There are homework assignments, a midterm and a final. The preciseweight of these components towards the final grade will be communicated on canvas. There is one resit opportunity for the full course. The grade for the homework does not count toward the grade of resit.Mandatory literature: Fourier Analysis, an Introduction, by Elias M. Stein and Rami Shakarchi. Princeton Lectures in Analysis I. Princeton University Press, 2003, ISBN-13: 978-0691113845.Bachelor Mathematics Year 2First year courses Single variable calculus, Multivariable calculus, Linear algebra, and Mathematical analysis.