- HOMEWORK PROBLEMS - Fall 2012
The homework refers to exercises from the textbook.
Homework 1 (due 8/28/12) :
Chapter 1 - 1.2, 1.4, 1.7.
Homework 2 (due 9/4/12) :
Work in teams, with Yuridia-David a new team, all the others the same).
Turn in problems 1. and [2. or 3.]:
- Show that uniform limit of continuous functions is continuous
- Show that if f is continuous on [a,b] then f is Riemann
integrable on [a,b].
- Show that if f_n is a sequence of Riemann integrable functions on
[a,b] that converges uniformly to f on [a,b] then f is Riemann
Integrable and the limit of the integrals is the integral of
f (Thm 2.53).
Homework 3 (due 9/11/12) :
Chapter 3 Exercise 3.11 in p.62 and exercise 4.18 p.89.
Homework 4 (due 9/18/12) :
This homework is a group work (due Tu 9/18/2012): 5 teams (3 people on each team):
One solution set turn in per team, all the members must be aware of what is being submitted, please acknowledge sources used: books, internet, etc.
- Team 1: David, and Cameron
- Team 2: Matt, Audrey.
- Team 3: Dusty, Jared, and James
- Team 4: Wang, Anastassiya, and Christopher
- Team 5: Vishnu, Yuri, and Craig.
- Exercise 3.25 (plucked string)
- Exercise 4.5 (the L^1 norms of D_N are not uniformly (in N) bounded, they grow like log N.
Homework 5 (due on Thursday 9/27/2012):
- Exercises 4.16 and 4.17.
Homework 6 (due Tuesday October 9, 2012):
- Proof of the Cauchy-Schwarz inequality
- Exercise 5.8 (show that the space of little ell 2 of square
summable sequences is complete).
Homework 7 (due 10/23/12):
- Exercises: 6.3, 6.13, 6.14, 6.19, 6.35.
Homework 8 (due 11/06/12):
- Exercise 7.11 (Gaussian is its own Fourier transform)
- Exercise 7.20 (Time Frequency dictionary convolution becomes
product and viceversa)
- Exercise 7.29 (practice use of Time Frequency dictionary)
Homework 9 (due 11/13/2012):
- Exercise 8.26 (finish Time-Frequency dictionary in S')
- Exercise 8.30 (calculus with the delta distribution)
- Exercise 8.33 (approximations of identity converge to delta
- Bonus: Exercise 8.46 (assuming Theorem 8.44)
Final Projects Fest
- Tuesday Dec 4th, 2012 (with snacks and coffee)
- 9:00-9:30 Monsters I: Nowhere Differentiable Functions (Yuri and Audrey)
- 9:35-10:05 Monsters II: A continuous functions whose partial Fourier sums diverge at a zero (David and Matt)
- 10:10-10:40 Weyl's equidistribution theorem (Dusty)
- Thursday Dec 6th, 2012 (with snacks and coffee)
- 9:00-9:25 Fourier Analysis on Groups (Cameron)
- 9:30-9:55 Averaging and Summability Methods (Bishnu and Craig)
- 9:55-10:10 Snacks and fill evaluation forms
- 10:10-10:40 Isoperimetric Problem (James and Chris)
- Tuesday Dec 11th, 2012 (with snacks and coffee)
- 8:30-8:45 Bowl of kernels (Wang)
- 8:50-9:30 Wavelets in action (Anastassiya and Wang)
- The end ;-)
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of Mathematics and Statistics, University
of New Mexico
Last updated: December 4, 2012