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: Laplace equation
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, 3pm - 6pm Final (exam code 02)

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)