Planned

Fri 04/23: Ch 6, pp. 204207: Radon transform: uniqueness and reconstruction.

Wed 04/21: Ch 6, pp. 201204: Radon transform in
R^{3}

Mon 04/19: Ch 6, pp. 198201: Radon transform, Xray transform in
R^{2}.
Covered

Fri 04/16: Review for Midterm Exam

Wed 04/14: Ch 6, pp. 196198: Radial symmetry and Bessel functions.

Mon 04/12: Ch 6, pp. 175184: Convolutions, Plancherel formula, Fourier inversion formula

Fri 04/09: Ch 6, pp. 175184: Schwartz class. Definition and properties of Fourier transform. Gaussian functions.

Wed 04/07: Ch 6, pp. 175184: Integration on
R^{d}. Rotations. Polar (spherical) coordinates.

Mon 04/05: Ch 5, pp. 158 161: Heisenberg uncertainty principle

Fri 04/02: Ch 5, pp. 153158: Poisson summation formula, theta function, heat and Poisson kernels on the circle.

Wed 03/31: Ch 5, pp. 152153: Harmonic functions: mean value property, maximum principle, uniqueness (in bounded and unbounded domains)

Mon 03/29: Ch 5, pp. 149 152: Laplace's equation in a halfplane, Poisson kernel

Fri 03/26: Ch 5, pp. 146149: Heat equation on
R

Wed 03/24:Ch 5, pp. 144146: Weierstrass Approx. Theorem, heat equation on
R

Mon 03/22: Ch 5, pp. 142144: Plancherel Formula

Mon 03/15  Fri 03/19: Spring break

Fri 03/12: Cancelled (because of the Midterm Exam)

Wed 03/10: Ch 5, pp. 139142: Gaussian Kernels, Fourier Inversion Formula

Mon 03/08: Overview of Midterm Exam

Fri 03/05: Ch 5, pp. 136139: The Schwartz space (continued), Gaussian Functions.

Wed 03/03: Ch 5, pp. 134136: Definition of Fourier Transform, the Schwartz space.

Mon 03/01: Ch 5, pp. 129134: Integration on
R

Fri 02/26: Review for Midterm Exam

Wed 02/24: Ch 4, pp. 116120: Continuous nowhere differentiable function (continued), Heat equation on circle

Mon 02/22: Ch 4, pp. 113116: Continuous nowhere differentiable function

Fri 02/19: Ch 4, pp. 108112: Weyl's equidistribution theorem continued.

Wed 02/17: Ch 4, pp. 104108: Isoperimetric inequality (finish), Weyl's equidistribution theorem

Mon 02/15: Ch 4, pp. 100104: Curves, lengths, and area, Isoperimetric inequality (start)

Fri 02/12: Ch 3, pp. 8587: Finish the counterexample of diverging Fourier series.

Wed 02/10: Ch 3, pp. 8486: Counterexample of diverging Fourier series, breaking the symmetry

Mon 02/08: Ch 3, pp. 8083: Parseval's identity, back to pointwise convergence, localization

Fri 02/05: Ch 3, pp. 7580: Hilbert and PreHilbert spaces, meansquare convergence

Wed 02/03: Ch 3, pp. 7074: Review of Vector spaces and inner products

Mon 02/01: Ch 2, pp. 5358: Abel means and summation, Poisson kernel and Dirichlet problem.

Fri, 01/29: Ch 2, pp. 4853: Good kernels, Cesaro means and summation, Fejer kernel.

Wed, 01/27: Ch 2, pp. 4448: Convolutions

Mon, 01/25: Ch 2, pp. 3944 : Uniqueness of Fourier series

Fri, 01/22: Ch 2, pp. 2933: Riemann integrable functions, functions on unit circle, pp. 3438: Definition of Fourier series, Dirichlet and Poisson kernels.

Wed, 01/20: Ch 1, pp. 1823: Heat equation, Laplace's equation.

Mon, 01/18: no class (MLK day)

Fri, 01/15: Ch 1, pp. 1518: Fourier series, plucked string.

Wed, 01/13: Ch 1, pp. 1015: D'Alembert's formula, standing waves, separation of variables, Fourier sine series

Mon, 01/11: Ch 1, pp. 110: Simple harmonic motion, derivation of wave equation, traveling waves.