Dates |
Lectures |
Topics |
| Chapter 5. Differentiation. | ||
| 1/5 | Lecture 1 | Introduction. The derivative of a real function. |
| 1/7 | Lecture 2 | Derivatives and properties. Mean value theorems. |
| 1/9 | Lecture 3 | Continuity and derivatives. Intermediate value property. |
| 1/12 | Lecture 4 | L'Hopital's rule. |
| 1/14 | Lecture 5 |
Taylor's theorem. Vector valued functions. Homework 1 due. |
| Chapter 6. Riemann Integral. | ||
| 1/16 | Lecture 6 | Definition of the integral. |
| 1/19 | No class. | MLK Day. |
| 1/21 | Lecture 7 |
Integration of continuous functions.
Homework 2 due. |
| 1/23 | Lecture 8 | Propreties of the integral. |
| 1/26 | Lecture 9 | Propreties of the integral. |
| 1/28 | Lecture 10 |
Midterm 1. |
| 1/30 | Lecture 11 | Integration and differentiation. |
| Chapter 7. Sequences and series of functions. | ||
| 2/2 | Lecture 12 | Sequences and series of functions. |
| 2/4 | Lecture 13 |
Uniform convergence.
Homework 3 due. |
| 2/6 | Lecture 14 | Uniform convergence and continuity. |
| 2/9 | Lecture 15 | Uniform convergence and integration. |
| 2/11 | Lecture 16 |
Uniform convergence and differentiation.
Homework 4 due. |
| 2/13 | Lecture 17 | Equicontinuity. |
| 2/16 | No class. | Presidents' Day. |
| 2/18 | Lecture 18 |
Equicontinuity. Arzela-Ascoli.
Homework 5 due. |
| 2/20 | Lecture 19 | Stone-Weierstrass. |
| 2/23 | Lecture 20 | Stone Weierstrass. |
| 2/25 | Lecture 21 | Stone-Weierstrass. |
| 2/27 | Lecture 22 |
Midterm 2 |
| Chapter 8. Special functions. | ||
| 3/2 | Lecture 23 | Power series. |
| 3/4 | Lecture 24 |
Exponential and logarithm.
Homework 6 due. |
| 3/6 | Lecture 25 | Trigonometric functions. |
| 3/9 | Lecture 26 | Fourier Series. |
| 3/11 | Lecture 27 |
Fourier Series.
Homework 7 due. |
| 3/13 | Lecture 28 | Fourier Series. |
| 3/20 | Final Exam. |