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  
Tue, 04/14* Ch 5, pp. 158-161: Heisenberg uncertainty principle  
Thur, 04/09* Ch 5, pp. 153-155, 156-158: Poisson summation formula, heat kernels  
Tue, 04/07* Ch 5, pp. 149-153: Laplace’s equation in a halfplane, Poisson kernel, Harmonic functions: mean value property, maximum principle  
Thur, 04/02 Ch 5, pp. 146-149: Heat equation on $\mathbb{R}$  
Tue, 03/31 Ch 5, pp. 142-144, 145-146: Convolutions, Plancherel Formula, Extensions to larger classes of functions, Heat equation on $\mathbb{R}$  
Thur, 03/26 Ch 5, pp. 139-142: Gaussians as good kernels, Fourier Inversion Formula, Convolutions  
Tue, 03/24 Ch 5, pp. 135-139: Fourier transform on the Schwartz space, Gaussians  
Thur, 03/19 No class (Spring Break)  
Tue, 03/17 No class (Spring Break)  
Thur, 03/12 No class (canceled to compensate for Mideterm Exam 1)  
Tue, 03/10 Midterm Exam 1, 8:00-9:30pm, in KNOY B033  
Tue, 03/10 Ch 5, pp. 129-134: Integration on $\mathbb{R}$, Definition of Fourier Transform.  
Thur, 03/05 Review for Midterm Exam 1  
Tue, 03/03 Ch 4, pp. 116-120: Continuous nowhere differentiable function (finish), Heat equation on circle  
Thur, 02/26 Ch 4, pp. 109-116: Weyl’s equidistribution theorem (finish), Continuous nowhere differentiable function  
Tue, 02/24 Ch 4, pp. 104-109: Isoperimetric inequality (finish), Weyl’s equidistribution theorem  
Thur, 02/19 Ch 4, pp. 100-104: 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