Classes (as well as the midterm and final) are MWF 9-9:50 in
MS 6221. Tutorials are Th 9-9:50 in MS 6221.
We will be following the textbook closely. It is strongly recommended
that you read textbook concurrently with the lectures; there is certainly no
harm in reading ahead, also. For similar reasons it is strongly
recommended that you perform all the homework on time, and preferably by your
own resources.
Week |
Monday |
Wednesday |
Thursday |
Friday |
0 |
|
|
|
Jan 9 (*): pp 30-34 Complex numbers, Riemann integral |
1 |
Jan 12 (*): pp 34-39 Fourier series, trig polynomials |
Jan 14 (*): pp 39-42 Uniform convergence; injectivity of FS |
Jan 15 No HW due |
Jan 16 (*): pp 42-44 Convergence results; FS and differentiation |
2 |
Jan 19 Martin Luther King |
Jan 21 (*): pp 44-48 FS and convolution; Dirichlet kernel |
Jan 22 HW 1 due |
Jan 23: pp 48-51 Convolution with good kernels |
3 |
Jan 26: pp 51-54 Gibbs phenomenon; Fejer summation |
Jan 28: pp 54 Uniform approximation |
Jan 29 HW 2 due |
Jan 30: pp 70-76 Inner product spaces, Fourier basis |
4 |
Feb 2: pp 76-81 Plancherel and Parseval theorems |
Feb 4: pp 101-105 Applications of Fourier series |
Feb 5 HW 3 due |
Feb 6: pp 106-113 More applications |
5 |
Feb 9 Leeway/Review |
Feb 11 Midterm |
Feb 12 No HW due |
Feb 13: pp 129-135 Fourier integrals; Schwartz functions |
6 |
Feb 16 President’s Day |
Feb 18: pp 136-137 Algebraic structure of FT |
Feb 19 No HW due |
Feb 20: pp 138-140 The FT and Gaussians |
7 |
Feb 23: pp 140-142 Fourier inversion formula |
Feb 25: pp 142-145 Convolutions and Plancherel theorem |
Feb 26 HW 4 due |
Feb 27: pp 175-180 Integration in several variables |
8 |
Mar 1: pp 180-184 FT in several variables |
Mar 3: pp 145-149 PDE application: heat equation |
Mar 4 HW 5 due |
Mar 5: pp 149-153 PDE application: |
9 |
Mar 8: Notes FT and ODE; Dirac delta function |
Mar 10: pp 219-223 Finite Fourier transform |
Mar 11 HW 6 due |
Mar 12: 224-226 Fast Fourier Transform |
10 |
Mar 15: Notes Fourier and Laplace transforms |
Mar 17: pp 153-154 Poisson Summation Formula |
Mar 18(**) HW 7 due |
|
Finals Week |
|
Mar 24, |
|
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FS = Fourier series
FT = Fourier transform
HW = Homework
ODE = Ordinary differential equations
PDE = Partial differential equations
(*) These lectures will be taught by Christoph Thiele.
(**) No TA session on Mar 18 (end of quarter)