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]

Planned  
Fri, 04/29: Review for Final Exam
Wed, 04/27: Ch 6, pp. 188–192: Wave Equation in for
   
Covered  
Mon, 04/25: Ch 6, pp. 175-184: Convolutions, Plancherel formula, Fourier inversion formula, pp. 184–186: Wave Equation in
Fri, 04/22: Ch 6, pp. 175-184: Schwartz class, Definition and properties of Fourier transform, Rotations, Gaussian functions
Wed, 04/20: Review for Midterm Exam 2
Mon, 04/18: Ch 6, pp. 175-184: Integration on , Spherical (polar) coordinates
Fri, 04/15: Ch 5, pp. 158-161: Heisenberg uncertainty principle
Wed, 04/13: Ch 4, pp. 118-120: Heat equation on circle, Ch 5, pp. 156-157: Heat kernels
Mon, 04/11: Ch 5, pp. 152-155: Uniqueness for harmonic functions, Poisson summation formula
Fri, 04/08: Ch 5, pp. 151-152: Harmonic functions: mean value property
Wed, 04/06: Ch 5, pp. 149-151: Laplace’s equation in a halfplane, Poisson kernel
Mon, 04/04: Ch 5, pp. 147-149: Heat equation on ,
Fri, 04/01: Ch 5, pp. 145-147: Weierstrass Approx. Theorem, heat equation on
Wed, 03/30: Ch 5, pp. 143-144: Plancherel Formula
Mon, 03/28: Ch 5, pp. 141-144: Fourier inversion, Plancherel Formula
Fri, 03/25: Ch 5, pp. 138-141: Gaussians as good kernels, Fourier inversion
Wed, 03/23: Ch 5, pp. 134-137: Definition of Fourier Transform, the Schwartz space
Mon, 03/21: Ch 5, pp. 129-134: Integration on
Fri, 03/18: Spring break
Wed, 03/16: Spring break
Mon, 03/14: Spring break
Fri, 03/11: Ch 4, pp. 112-113: Weyl’s equidistribution theorem (finish), Midterm Exam 1 Discussion
Wed, 03/09: Ch 4, pp. 108-111: Weyl’s equidistribution theorem
Mon, 03/07: Ch 4, pp. 105-107: Weyl’s equidistribution theorem
Fri, 03/04: Ch 4, pp. 103-105: Isoperimetric inequality (finish)
Wed, 03/02: Review for Midterm Exam 1
Mon, 02/28: Ch 4, pp. 100-103: Curves, lengths, and area, Isoperimetric inequality (start)
Fri, 02/25: Ch 3, pp. 85-87: Finish the counterexample of diverging Fourier series
Wed, 02/23: Ch 3, pp. 84-86: Counterexample of diverging Fourier series, breaking the symmetry
Mon, 02/21: Ch 3, pp. 80-84: Riemann-Lebesgue lemma, back to pointwise convergence, localization
Fri, 02/18: Ch 3, pp. 76-80: Mean-square convergence, Parseval’s identity
Wed, 02/16: Ch 3, pp. 74-76: Hilbert and Pre-Hilbert spaces
Mon, 02/14: Ch 3, pp. 70-73: Review of Vector spaces and inner products
Fri, 02/11: Ch2, pp. 55-58, Poisson kernel and Dirichlet problem
Wed, 02/09: Ch 2, pp. 53-56: Fejer kernel, Abel means and summation, Poisson kernel
Mon, 02/07: Ch 2, pp. 48-52 Good kernels, Cesaro means and summation
Fri, 02/04: Snow day (no new material covered)
Wed, 02/02: Snow day (no new material covered)
Mon, 01/31: Ch 2, pp. 46-48 Convolutions, pp. 48-49: Good kernels
Fri, 01/28: Ch 2, pp. 44-48 Convolutions
Wed, 01/26: Ch 2, pp. 40-44: Uniqueness of Fourier series
Mon, 01/24: Ch 2, pp. 37-38: Partial sums, Dirichlet and Poisson kernels, pp. 39-40 Uniqueness of Fourier series
Fri, 01/21: Ch 2, pp. 29–34: Riemann integrable functions, functions on unit circle, pp.34-36: Definition of Fourier series
Wed, 01/19: Ch 1, pp. 18-23: Heat equation, Laplace’s equation
Mon, 01/17: No Class (MLK day)
Fri, 01/14: Ch 1, pp. 14–18: Fourier sine series, Fourier series, plucked string
Wed, 01/12: Ch 1, pp. 8–14: traveling waves, D’Alembert’s formula, standing waves, separation of variables
Mon, 01/10: Ch 1, pp. 1–8: Simple harmonic motion, derivation of wave equation