| Lec. | Date | Topics | Sections |
|---|---|---|---|
| 1 | 1/12 | Sequences and convergence -- review. | 2.1, 2.2, 2.4, 2.6 |
| 2 | 1/14 | Lim sup and Lim inf. | 6.1 |
| - | 1/19 | -- MLK Day -- | |
| 3 | 1/21 | Lim sup and Lim inf. Series of real constants. |
6.1 6.2 |
| 4 | 1/26 | Tests for convergence. | 6.2, etc. |
| 5 | 1/28 | Absolute convergence. | 6.2 |
| 6 | 2/2 | Continuous and differentiable functions -- review. | 3.1, 3.2, 4.1 |
| 7 | 2/4 | Taylor's Theorem. L'Hospital's rule. | 4.3 |
| 8 | 2/9 | Inverse functions. | 4.5 |
| 9 | 2/11 | Inverse functions. | 4.5 |
| 10 | 2/16 | Functions of two variables. | 4.6 |
| 11 | 2/18 | Functions of two variables. | 4.6 |
| 12 | 2/23 | Review | |
| 13 | 2/25 | Exam 1 | |
| 14 | 3/2 | Pointwise and uniform convergence. | 5.1 |
| 15 | 3/4 | Limit theorems. | 5.2 |
| 16 | 3/9 | The supremum norm. | 5.3 |
| 17 | 3/11 | Metric Spaces. | 5.6 |
| - | 3/16-21 | -- Spring break -- | |
| 18 | 3/23 | Convergence. Complete metric spaces. | 5.6, 5.7 |
| 19 | 3/25 | The Contraction Mapping Principle. | 5.7 |
| 20 | 3/30 | Applications of the Contraction Mapping Principle. | (5.4) |
| 21 | 4/1 | Review | |
| 22 | 4/6 | Exam 2 | |
| 23 | 4/8 | Exam discussion. Limits and continuity in metric spaces |
6.3 |
| 24 | 4/13 | Series of functions and convergence. | 6.3 |
| 25 | 4/15 | Weierstrass M-test. Integrating and differentiating series of functions. |
6.3 |
| 26 | 4/20 | Power series. | 6.4 |
| 27 | 4/22 | Taylor series. | 6.4 |
| 28 | 4/27 | Fourier series. | |
| 29 | 4/29 | Review |