Week 36: Sections 1.1-3 and 2.1 in [GF]; overview, motivation with partial differential equations (PDE), separation of variables, Fourier series and their convergence (Obs! We prove the Corollary 2.1 in more general form.)
Week 37: 2.2-6; Dirichlet kernel, Gibbs phenomenon; differentiation and properties, applications and further remark
Week 38: 3.1-3; inner product, L2 spaces
Week 39: 3.4-5; best approximation, Sturm-Liouville problems, some solution methods for PDE
Week 40: 4.1-4; more solution methods, the Dirichlet problem
Week 41: 7.1-2; convolution, the Fourier transform
Week 42: 7.3; applications of the Fourier transform, signal analysis
Week 43: Questions, exam