Here you will find information about the material that was already covered or will be covered in the next few lectures.

Chapters and pages are from the textbook [Stein-Shakarchi].

Star * after the date indicates planned content.

Date Content
Thur, 02/19* Ch 4, pp. 100-105: Curves, lengths, and area, Isoperimetric inequality
Tue, 02/17* Ch 3, pp. 84-87: Counterexample of diverging Fourier series, breaking the symmetry
Thur, 02/12* Ch 3, pp. 79-84: Mean-square convergence, Parseval’s identity, back to pointwise convergence, localization, Counterexample of diverging Fourier series (start)
Tue, 02/10* Ch 3, pp. 74-79: Hilbert and Pre-Hilbert spaces, Best Approximation, Bessel’s inequality
Thur, 02/05 Ch 2, pp. 56-58: Dirichlet problem, Ch 3, pp. 70-74: Review of Vector spaces and inner products.
Tue, 02/03 Ch 2, pp. 50-56: Good kernels, Cesaro means and summation, Fejer kernel, Abel means and summation, Poisson kernel
Thur, 01/29 Ch 2, pp. 44-51: Convolutions, good kernels
Tue, 01/27 Ch 2, pp. 39-44: Uniqueness of Fourier series
Thur, 01/22 Ch 2, pp. 33-38: Functions on unit circle, Definition of Fourier series, Dirichlet and Poisson kernels.
Tue, 01/20 Ch 1, pp. 18-23: Heat equation, Laplace’s equation. Ch 2, pp. 29-33: Riemann integrable functions
Thur, 01/15 Ch 1, pp. 11-18: Standing waves, separation of variables, Fourier sine series, Fourier series, plucked string
Tue, 01/13 Ch 1, pp. 1-11: Simple harmonic motion, derivation of wave equation, traveling waves, D’Alembert’s formula