- Understand the concepts of "periodic function" and "trigonometric polynomial";
- Calculate Fourier coefficients of simple functions, such as (trigonometric) polynomials and indicator functions;
- Write formal Fourier series and understand their relation to convergent series;
- Review necessary convergence concepts (pointwise, uniform) in this context;
- Understand and visualize convergence/divergence using simple functions (linear, quadratic);
- Understand and be able to prove various classical convergence and approximation theorems (Fejér, Weierstrass, Riemann-Lebesgue, Dirichlet);
- Know the connection to Hilbert space theory;
- Work with the Fourier transform (definition, basic properties, inversion, Plancherel's theorem);
- Know various applications: heat equation, wave equation, Weyl's theorem on equidistributed sequences, Heisenberg's uncertainty principle, isoperimetric inequality of the circle;
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periodic functions, Fourier coefficients, Fourier series, classical convergence and approximation theorems (Fejér, Weierstrass, Riemann-Lebesgue, Dirichlet), Fourier transform, inversion formula, applications in other mathematical disciplines
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