| Date | Topic | Reading | Problems |
|---|---|---|---|
| 8/27/03 | In the beginning... | paper folding problem (described in class) | |
| 8/29/03 | Rational versus real numbers | pages 1-17 | some problems of my own devising; pp 21-23: 1, 2, 6, 8, 10 |
| 9/1/03 | Real numbers (continued) | ||
| 9/3/03 | Cardinality | pp 26-30 | extra credit problem about decimal expansions |
| 9/5/03 | Cardinality (cont) | pp 30-36 | my problems ; pp 43-46: 2, 4 |
| 9/8/03 | Metric spaces | ||
| 9/10/03 | Compact sets | pp36-43 | |
| 9/12/03 | Compact sets (cont) | my problems ; pp43: 6, 9, 11 (explain what fails if not), 12, 23 | |
| 9/15/03 | Connected sets, Cantor sets | ||
| 9/17/03 | Convergent Sequences | pp47-51 | |
| 9/19/03 | Subsequences | my problems ; p44: 20; pp78-82: 1, 2; my solutions | |
| 9/22/03 | Limsup, Liminf | pp52-57 | |
| 9/24/03 | Cauchy sequences | ||
| 9/26/03 | Series | pp58-63 | p78: 4, 14abc, 16ab, 20, 23; my solutions |
| 9/29/03 | e; the root and ratio tests | pp64-69, look at page 78: 6abc*, 7, 11*, 15*, 17, 21*, 22*, 23* | |
| 10/1/03 | Absolute versus conditional convergence | pp71-78, continue looking at problems from Monday | |
| 10/3/03 | Exam review | Solution to p82: 22 | |
| 10/6/03 | Continuity | pp83-89 | |
| 10/8/03 | Continuous images of compact and connected sets | look at pp98-102: 1, 3, 4, 5, 7, 8, 12, 13 | |
| 10/10/03 | No class | my problems ; p98: 2, 6, 10, 14; my solutions | |
| 10/13/03 | Discontinuities, monotonicity | pp94-98; look at pp98-102: 16, 18, 19, 23, 26 | |
| 10/15/03 | Differentiation | pp104-111 | |
| 10/17/03 | Differentiation (cont) | look at p115-119: 1, 2, 3, 4, 11 | pp100-101: 17 (treat only the cases f(x+) < f(x-)
and f(x+) = f(x-) < f(x); the others are similar ), 23; p114: 6, 9, 13abcd, 14, 19ac, 22abc; my solutions |
| 10/27/03 | Differentiation (cont) | look at p115-119: 1, 2, 3, 4, 11 | |
| 10/29/03 | The Riemann Integral | pp120-134 | |
| 10/31/03 | Riemann Integration (cont) | ||
| 11/3/03 | Integration (cont) | look at pp138: 2, 5 | my problems; pp138: 7; my solutions |
| 11/5/03 | Solutions to homework 7 | ||
| 11/7/03 | Sequences and series of functions | read pp143-149 | |
| 11/10/03 | Uniform convergence and continuity | read pp149-154 | my problems; pp139: 10abc, pp165: 1, 4; my solutions |
| 11/12/03 | Uniform convergence, differentiation, and integration | ||
| 11/14/03 | Power series | read pp172-178 | |
| 11/17/03 | Power series (cont) | my problems; pp165-166: 2 (just the product part), 3, 9; my solutions | |
| 11/19/03 | Yet more on power series | ||
| 11/21/03 | (Double feature) Ordinary differential equations | read pp220-221, look at p170: 25 | |
| 11/24/03 | (Double feature) ODEs: existence and uniqueness theorm | Last homework assignment! my solutions | |
| 11/26/03 | (Double feature) Yet more ODEs | ||
| 11/27/03 - 12/5/03: lull | |||
| 12/8/03 | TCEs, etc | ||
| 12/10/03 | Fundamental theorem of algebra | ||