| Lec. | Date | Topics | Chapter |
|---|---|---|---|
| 1 | 1/7 | Pointwise convergence and uniform convergence of a sequence of functions. |
7 |
| 2 | 1/10 | Uniform convergence. The supremum norm. | 7 |
| 3 | 1/14 | Uniform convergence and integration, differentiation. | 7 |
| 4 | 1/17 | Uniform convergence of a series of functions. Equicontinuous families of functions. |
7 |
| - | 1/21 | -- MLK Day -- | |
| 5 | 1/23 | Equicontinuous families of functions. | 7 |
| 6 | 1/28 | Stone-Weierstass Theorem. Taylor's Theorem. | 7, 8 |
| 7 | 1/30 | Taylor series. Power series. Exponential function. | 8 |
| 8 | 2/4 | Fourier series. | 8 |
| 9 | 2/6 | Orthogonal series. Convergence of the Fourier series. | 8 |
| 10 | 2/11 | Vector spaces and linear transformations. | 9 |
| 11 | 2/13 | Linear transformations. | 9 |
| 12 | 2/18 | Norm of a linear transformation. Differential. | 9 |
| 13 | 2/20 | Differential and partial derivatives. | 9 |
| 14 | 2/25 | Gradient and directional derivatives. | 9 |
| 15 | 2/27 | Bounded derivative. Contraction Principle. | 9 |
| 16 | 3/3 | Inverse Function Theorem. | 9 |
| 17 | 3/5 | Implicit Function Theorem. | 9 |
| - | 3/10-16 | -- Spring break -- | |
| 18 | 3/17 | Midterm Exam | |
| 19 | 3/19 | Exam discussion. Examples. | |
| 20 | 3/24 | Rings and sigma-rings. Set functions. | 11 |
| 21 | 3/26 | Regular set functions. Outer measure. | 11 |
| 22 | 3/31 | Lebesgue measure. | 11 |
| 23 | 4/2 | Lebesgue measure. | 11 |
| 24 | 4/7 | Borel sets, sets of measure 0, and measurable sets. | 11 |
| 25 | 4/9 | Measurable spaces. Measurable functions. | 11 |
| 26 | 4/14 | Simple functions. Definition of Lebesgue integral. | 11 |
| 27 | 4/16 | Properties of Lebesgue integral. | 11 |
| 28 | 4/21 | Properties of Lebesgue integral. | 11 |
| 29 | 4/23 | Properties of Lebesgue integral. Comparison with Riemann integral. |
11 |