| Week | Date | Contents | Homeworks |
| 1 | 2/7 ~ 2/11 | Background knowledge, Infinite sets, Metric spaces, Open and closed sets | -- |
| 2 | 2/14 ~ 2/18 | Compactness, Heine-Borel theorem, Least upper bound |
Homework 1 (due: 2/18) and Solution |
| 3 | 2/21 ~ 2/25 | Completeness, Upper and lower limits, Convergece of series |
Homework 2 (due: 2/25) and Solution |
| 4 | 2/28 ~ 3/4 | Power series, Continuous functions |
Homework 3 (due: 3/04) and Solution |
| 5 | 3/7 ~ 3/11 | Uniform continuity, One-sided limits, Types of discontinuities, Intermediate value theorem |
Homework 4 (due: 3/11) and Solution |
| 6 | 3/14 ~ 3/18 | Differentiation, Mean value theorem, L'Hospital's rule |
Homework 5 (due: 3/18) and Solution |
| 7 | 3/21 ~ 3/25 | Taylor's formula with remainder, Riemann-Stieltjes integration |
Homework 6 (due: 3/25) and Solution |
| 8 | 3/28 ~ 4/1 | Midterm exam; Wednesday March 30th at 9am | Problem, Solution, Score and Histogram |
| 9 | 4/4 ~ 4/8 | Fundamental theorem of calculus, Bounded variation, Integration by parts |
Homework 7 (due: 4/8) and Solution |
| 10 | 4/11 ~ 4/15 | Change of variables, Mean value theorem for integrals, Improper integrals |
Homework 8 (due: 4/15) and Solution |
| 11 | 4/18 ~ 4/22 | Uniform convergence, Limit operations, Weierstrass M-test |
-- |
| 12 | 4/25 ~ 4/29 | Arzela-Ascoli theorem, Weierstrass approximation theorem |
-- |
| 13 | 5/2 ~ 5/6 | Measurable sets, Lebesgue measure, Measurable functions |
-- |
| 14 | 5/9 ~ 5/13 | Lusin's theorem, Egoroff's theorem, Lebesgue integral |
Homework 9 (due: 5/13) and Solution |
| 15 | 5/16 ~ 5/20 | Fatou's lemma, Lebesuge dominated convergence theorem, Lp spaces |
Homework 10 (due: 5/20) and Solution |
| 16 | 5/23 ~ 5/27 | Final exam; Wednesday May 25th at 9am |
Problem, Solution, Score and Grade |
Last modified on May 30, 2011.