## Monday, April 28, 2014

### Course Log

Covered
05/01: Review for Final Exam
04/29:  Ch 6, pp 192-196, 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 187-192, Energy conservation, Wave equation in $\mathbb{R}^3\times\mathbb{R}$ (start)
- 04/22: Overview of Midterm 2, Ch 6, pp 184-187, Wave equation in $\mathbb{R}^d\times\mathbb{R}$
- 04/17: Review for Midterm 2
- 04/15: Ch 6, pp 175-184, Fourier transform in $\mathbb{R}^d$
04/10: Ch 5, pp. 153-161: 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. 147-150: Heat equation on $\mathbb{R}$, Laplace's equation in a halfplane, Poisson kernel
04/01: Ch 5, pp. 142-147: Plancherel Formula, Heat equation on $\mathbb{R}$
03/27: Ch 5, pp. 139-142: Gaussian Functions, Fourier Inversion Formula
03/25: Ch 5, pp. 134-138: 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. 118-120: Heat equation on circle, Ch 5, pp. 129-134: Integration on $\mathbb{R}$Definition of Fourier Transform
03/06: Ch 4, pp. 113-118: Continuous nowhere differentiable function
03/04: Ch 4, pp. 105-113: Weyl's equidistribution theorem
- 02/27: Review for Midterm Exam 1
02/25: Ch 4, pp. 100-105: Curves, lengths, and area, Isoperimetric inequality
02/20: Ch 3, pp. 84-87: Counterexample of diverging Fourier series, breaking the symmetry
02/13: Ch 3, pp. 79-84: Mean-square convergence, Parseval's identity, back to pointwise convergence, localization,  Counterexample of diverging Fourier series (start)
02/11: Ch 3, pp. 74-79:  Hilbert and Pre-Hilbert spaces, Best Approximation, Bessel's inequality
02/06: Ch 2, pp. 56-58: Dirichlet problem, Ch 3, pp. 70-74: Review of Vector spaces and inner products.
02/04: Ch 2, pp. 51-56: Cesaro means and summation, Fejer kernel, Abel means and summation, Poisson kernel
- 01/30: Ch 2, pp. 45-51: Convolutions, good kernels
- 01/28: Ch 2, pp. 39-44: Uniqueness of Fourier series
- 01/23: Ch 2, pp. 34-38: Definition of Fourier series, Dirichlet and Poisson kernels.
- 01/21: Ch 1, pp. 18-23: Heat equation, Laplace's equation. Ch 2, pp. 29-33: Riemann integrable functions, functions on unit circle
- 01/16: Ch 1, pp. 11-18: Standing waves, separation of variables, Fourier sine series, Fourier series, plucked string.
- 01/14: Ch 1, pp. 1-11: Simple harmonic motion, derivation of wave equation, traveling waves, D'Alembert's formula