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  
Thur, 05/02: Review/Discussion for Final, 7-9pm in PRCE 277
   
Covered  
Thur, 04/25: Ch 6, pp 189-196, Wave Equation in \(\mathbb{R}^d\times\mathbb{R}\) for \(d=3,2\)
Tue, 04/23: Ch 6, pp 183-189, Fourier transform in $\mathbb{R}^d$; Heat Equation and Wave Equation in \(\mathbb{R}^d\times\mathbb{R}\)
Thur, 04/18: Ch 6, pp 175-183, Fourier transform in $\mathbb{R}^d$
Tue, 04/16: Review/Discussion for Midterm 2
Thur, 04/11: Ch 5, pp. 158-161: Heisenberg uncertainty principle
Tue, 04/09: Ch 5, pp. 151-155, 156-157: Laplace’s equation uniqueness (in bounded and unbounded domains), Poisson summation formula, heat kernels
Thur, 04/04: Ch 5, pp. 150-153: Laplace’s equation in a halfplane, Poisson kernel, Harmonic functions: mean value property, maximum principle
Tue, 04/02: Ch 5, pp. 147-150: Heat equation on $\mathbb{R}$ (finish), Laplace’s equation in a halfplane, Poisson kernel
Thur, 03/28: Ch 5, pp. 144, 145-147: Extensions to larger classes of functions, Heat equation on $\mathbb{R}$
Tue, 03/26: Ch 5, pp. 142-144: Plancherel Formula
Thur, 03/21: Ch 5, pp. 139-142: Gaussian Functions, Fourier Inversion Formula
Tue, 03/19: Ch 5, pp. 134-138: Fourier transform on the Schwartz space, Gaussian Functions (start)
Thur, 03/14: Spring Break
Tue, 03/12: Spring Break
Thur, 03/07: Ch 4, pp. 118-120: Heat equation on circle, Ch 5, pp. 129-134: Integration on $\mathbb{R}$, Definition of Fourier Transform
Tue, 03/05: Review/Discussion for Midterm 1
Thur, 2/29: Ch 4, pp. 113-118: Continuous nowhere differentiable function
Tue, 02/27: Ch 4, pp. 105-113: Weyl’s equidistribution theorem
Thur, 02/22: Ch 4, pp. 100-105: Curves, lengths, and area, Isoperimetric inequality
Tue, 02/20: Ch 3, pp. 84-87: Counterexample of diverging Fourier series
Thur, 02/15: Ch 3, pp. 81-84: Back to pointwise convergence, localization, breaking the symmetry
Tue, 02/13: Ch 3, pp. 76-81: Mean-square convergence, Best Approximation, Bessel’s inequality, Parseval’s identity, Riemann-Lebesgue lemma
Thur, 02/08: Ch 3, pp. 72-76: Inner products, Hilbert and Pre-Hilbert spaces
Tue, 02/06: Ch 2, pp. 57-58, Ch 3, pp. 70-72: Dirichlet problem, Review of Vector spaces and inner products.
Thur, 02/01: Ch 2, pp. 54–57: Uniform Approximation by Trig Polynomials, Abel means and summation, Poisson kernel, Dirichlet problem
Tue, 01/30: Ch 2, pp. 48–53: Good kernels, Cesaro means and summation, Fejer kernel
  Note: Will hold remotely; links to video and notes will be emailed before the scheduled class time. They will also be posted in Brightspace module “Remote Classes.”
Thur, 01/25: Ch 2, pp. 41–48: Uniqueness of Fourier series (finish), Uniform convergence (quick review), Convolutions
Tue, 01/23: Ch 2, pp. 33-34, 39–41: Functions on unit circle, Uniqueness of Fourier series
  Note: Held remotely due to Purdue’s closure; links to video and notes were emailed. Also posted in Brightspace module “Remote Classes.”
Thur, 01/18: Ch 2, pp. 29–38: Riemann integrable functions, definition of Fourier series, Dirichlet and Poisson kernels.
Tue, 01/16: Ch 1, pp. 16–23: Plucked string example, Fourier series, Heat equation, Laplace’s equation.
Thur, 01/11: Ch 1, pp. 10–16: D’Alembert’s formula, standing waves, separation of variables, Fourier sine series.
Tue, 01/09: Ch 1, pp. 1–10: Simple harmonic motion, derivation of wave equation, traveling waves