Covered

05/01: Review for Final Exam

04/29: Ch 6, pp 192196, Wave equation in $\mathbb{R}^3\times\mathbb{R}$ (finish), Huygens principle, Wave equation in $\mathbb{R}^2\times\mathbb{R}$

04/24: Ch 6, pp 187192, Energy conservation, Wave equation in $\mathbb{R}^3\times\mathbb{R}$ (start)

04/22: Overview of Midterm 2, Ch 6, pp 184187, Wave equation in $\mathbb{R}^d\times\mathbb{R}$

04/17: Review for Midterm 2

04/15: Ch 6, pp 175184, Fourier transform in $\mathbb{R}^d$

04/10: Ch 5, pp. 153161: Poisson summation formula, theta function, heat and Poisson kernels, the Heisenberg uncertainty principle

04/08: Ch 5, pp. 150 153: Laplace's equation in a halfplane, Poisson kernel, Harmonic functions: mean value property, maximum principle, uniqueness (in bounded and unbounded domains).

04/03: Ch 5, pp. 147150: Heat equation on $\mathbb{R}$, Laplace's equation in a halfplane, Poisson kernel

04/01: Ch 5, pp. 142147: Plancherel Formula, Heat equation on $\mathbb{R}$

03/27: Ch 5, pp. 139142: Gaussian Functions, Fourier Inversion Formula

03/25: Ch 5, pp. 134138: Fourier transform on the Schwartz space, Gaussian Functions (started)

03/18  03/20: Spring break

03/13: Overview of Midterm 1

03/11: Ch 4, pp. 118120: Heat equation on circle, Ch 5, pp. 129134: Integration on $\mathbb{R}$
, Definition of Fourier Transform

03/06: Ch 4, pp. 113118: Continuous nowhere differentiable function

03/04: Ch 4, pp. 105113: Weyl's equidistribution theorem

02/27: Review for Midterm Exam 1

02/25: Ch 4, pp. 100105: Curves, lengths, and area, Isoperimetric inequality

02/20: Ch 3, pp. 8487: Counterexample of diverging Fourier series, breaking the symmetry

02/13: Ch 3, pp. 7984: Meansquare convergence, Parseval's identity, back to pointwise convergence, localization, Counterexample of diverging Fourier series (start)

02/11: Ch 3, pp. 7479: Hilbert and PreHilbert spaces, Best Approximation, Bessel's inequality

02/06: Ch 2, pp. 5658: Dirichlet problem, Ch 3, pp. 7074: Review of Vector spaces and inner products.

02/04: Ch 2, pp. 5156: Cesaro means and summation, Fejer kernel, Abel means and summation, Poisson kernel

01/30: Ch 2, pp. 4551: Convolutions, good kernels

01/28: Ch 2, pp. 3944: Uniqueness of Fourier series

01/23: Ch 2, pp. 3438: Definition of Fourier series, Dirichlet and Poisson kernels.

01/21: Ch 1, pp. 1823: Heat equation, Laplace's equation. Ch 2, pp. 2933: Riemann integrable functions, functions on unit circle

01/16: Ch 1, pp. 1118: Standing waves, separation of variables, Fourier sine series, Fourier series, plucked string.

01/14: Ch 1, pp. 111: Simple harmonic motion, derivation of wave equation, traveling waves, D'Alembert's formula