Course Log
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 |