Real Analysis (honors)
Winter 2012
General Info | Day-to-day
Day to day: Reading, topics, homework
wk | date | reading | topic | homework | links |
1 | 1/4 | Ch I.1-4 | Sets | Ch I: 3ab, 5a, 7cf, 10ab | 1/6 | Ch II.1-2 | Ordered fields | Ch II: 2ab, 3, 6 |
2 | 1/9 | Ch II.3-4 | Least upper bound | Ch II: 10a, 11, 12, 13 | |
1/11 | Ch III.1 | Metric spaces | Ch III: 1ab | ||
1/13 | Ch III.2 | Open sets | Ch III: 3, 4, 5 | ||
1/16 Monday - Martin Luther King Jr. day | |||||
3 | 1/18 | Ch III.3 | Convergent seqn | Ch III: 8, 10, 11, 18 | |
1/20 | Ch III.4 | Complete spaces | Ch III: 24 | ||
4 | 1/23 | Ch III.5 | Compact spaces | Ch III: 32 | |
1/25 | Ch III.5 | Heine-Borel thm | Ch III: 35, 36, 37 | ||
1/27 | Ch III.6 | Connected spaces | Ch III: 38 | ||
5 | 1/30 | Ch IV.1 | Continuous fns | Ch IV: 1d, 2, 4 | |
2/1 | Ch IV.2 | Cont. fns and limits | (none) | ||
2/3 | Ch IV.3 | Rational fns | Ch IV: 9a | ||
6 | 2/6 | Ch IV.4 | Fns on compact set | Ch IV: 14ab [see example 2 in IV.1] | |
2/7 Tuesday x-hour: In-class exam | |||||
2/8 | Ch IV.5 | Fns on connected set | Ch IV: 29b | ||
2/10 Friday - Carnival holiday | |||||
7 | 2/13 | Ch IV.6 | Sequences of fns | Ch IV: 33ab | |
2/15 | Ch IV.6 | Sequences of fns | The Hilbert curve | Animation | |
2/17 | Ch V.1-3 | Derivatives | (none) | ||
8 | 2/20 | Ch V.4 | Taylor's thm | Ch V: 1b, 12 | |
2/22 | Ch VI.1-2 | Riemann integral | Ch VI: 11 | ||
2/24 | <Ch VI.3 | Integrability | Ch VI: 5, 8, 20 | Lecture notes | |
9 | 2/27 | Ch VI.4-5 | Fund. theorem | >Ch VI: 17 | |
2/29 | Ch VII.1 | Int/diff of seqn of fns | Ch VII: 1, 4 | ||
3/1 | Ch VII.2-3 | Infinite series | Ch VII: 8, 14, 41 | ||
10 | 3/5 | Ch VII.2-3 | Analytic functions | (none) | |
3/7 | Ch VI.5-VII.4 | The elementary fns | (none) | ||
3/10: Final take-home exam due |