Classes (as well as the midterm and final) are MWF 99:50 in
MS 6221. Tutorials are Th 99:50 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 3034 Complex numbers, Riemann integral 
1 
Jan 12 (*): pp 3439 Fourier series, trig polynomials 
Jan 14 (*): pp 3942 Uniform convergence; injectivity of FS 
Jan 15 No HW due 
Jan 16 (*): pp 4244 Convergence results; FS and differentiation 
2 
Jan 19 Martin Luther King 
Jan 21 (*): pp 4448 FS and convolution; Dirichlet kernel 
Jan 22 HW 1 due 
Jan 23: pp 4851 Convolution with good kernels 
3 
Jan 26: pp 5154 Gibbs phenomenon; Fejer summation 
Jan 28: pp 54 Uniform approximation 
Jan 29 HW 2 due 
Jan 30: pp 7076 Inner product spaces, Fourier basis 
4 
Feb 2: pp 7681 Plancherel and Parseval theorems 
Feb 4: pp 101105 Applications of Fourier series 
Feb 5 HW 3 due 
Feb 6: pp 106113 More applications 
5 
Feb 9 Leeway/Review 
Feb 11 Midterm 
Feb 12 No HW due 
Feb 13: pp 129135 Fourier integrals; Schwartz functions 
6 
Feb 16 President’s Day 
Feb 18: pp 136137 Algebraic structure of FT 
Feb 19 No HW due 
Feb 20: pp 138140 The FT and Gaussians 
7 
Feb 23: pp 140142 Fourier inversion formula 
Feb 25: pp 142145 Convolutions and Plancherel theorem 
Feb 26 HW 4 due 
Feb 27: pp 175180 Integration in several variables 
8 
Mar 1: pp 180184 FT in several variables 
Mar 3: pp 145149 PDE application: heat equation 
Mar 4 HW 5 due 
Mar 5: pp 149153 PDE application: 
9 
Mar 8: Notes FT and ODE; Dirac delta function 
Mar 10: pp 219223 Finite Fourier transform 
Mar 11 HW 6 due 
Mar 12: 224226 Fast Fourier Transform 
10 
Mar 15: Notes Fourier and Laplace transforms 
Mar 17: pp 153154 Poisson Summation Formula 
Mar 18(**) HW 7 due 

Finals Week 

Mar 24, 


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)