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 | L |
pp31-33 |   |
4/14/04 | L |
  |   |
4/16/04 | L |
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 |   |