Math 366 Assignments, Winter `04


Reading should be completed before class on the given date. Unless otherwise noted here or in class, homework problems should be completed and turned in at the beginning of class the Friday after they are assigned.

Date Topic Reading Problems
1/14/04 As I was saying last time... Rudin pp208-211  
1/16/04 Norm of a linear transformation 1st hwk, Solutions
1/19/04 Differentiation Rudin pp211-220  
1/21/04 Partial Derivatives    
1/23/04 Homework discussion   Homework 2, solutions
1/26/04 Chain Rule    
1/28/04 Inverse Function Theorem (statement and examples) Rudin pp220-223  
1/30/04 Inverse Function Theorem (proof)   Homework 3, solutions
2/2/04 Inverse Function Theorem proof    
2/4/04 Implicit Function Theorem    
2/6/04 Implicit Function Theorem (proof)   Homework 4 ; solutions
2/9/04 Submanifolds of R^n    
2/11/04 Submanifolds of R^n    
2/13/04 Polynomial approximation Rudin pp159-165 Homework 5; Solutions and Mathematica worksheet (or html version ) for last problem
2/16/04 The Stone Weierstrass Theorem (statement)    
2/18/04 Stone-Weierstrass (proof)    
2/20/04 Lebesgue Integration (overview) Beals notes, pp1-2 Homework 6; solutions
2/23/04 Outer measure Beals notes, pp3-4  
2/25/04 Measurable sets Beals notes, pp6-8  
2/27/04 Measurable sets (cont) Beals notes, pp9-11  
3/1/04 Measurable functions Beals pp13-15  
3/3/04 Exam 5-7 PM (no class)    
3/5/04 Measurable functions   Homework 7, solutions
3/15/04 Definition of Lebesgue integral Beals pp18-22  
3/17/04 A non-measurable set (Giampa) Beals page 12  
3/19/04 Two examples (Saviano) Beals pp16-17  
3/22/04 Definition of Lebesgue integral (cont)    
3/24/04 Banach-Tarski Theorem (Jenista) pp41-43  
3/26/04 Convergence Theorems pp24-25 Homework 8, solutions
3/29/04 Convergence Theorems (cont)    
3/31/04 Null sets page 27  
4/5/04 Riemann vs. Lebesgue integration pp28-30  
4/7/04 L1 pp31-33  
4/14/04 L1 (cont)    
4/16/04 L2 (cont) pp35-36  
4/19/04 Fourier series--Fejer and Dirichlet Kernels pp45-50 hwk probs p47: 1,2,3,4a
hwk probs p50: 1,3,4
4/21/04 Convergence theorems I pp52-57  
4/23/04 Picture show pp52-57  
4/26/04 Nick and Andrew    
4/28/04 Convergence theorems II---it all comes together pp58-59