Dates |
Lectures |
Topics |
| Chapter 5. Differentiation. | ||
| 4/3 | Lecture 1 | Introduction. The derivative of a real function. |
| 4/5 | Lecture 2 | Derivatives and properties. Mean value theorems. |
| 4/7 | Lecture 3 |
Continuity and derivatives. Intermediate value property.
Homework 1 due. |
| 4/10 | Lecture 4 | L'Hopital's rule. |
| 4/12 | Lecture 5 | Taylor's theorem. Vector valued functions. |
| Chapter 6. Riemann Integral. | ||
| 4/14 | Lecture 6 |
Definition of the integral.
Homework 2 due. |
| 4/17 | Lecture 7 | Integration of continuous functions. |
| 4/19 | Lecture 8 | Propreties of the integral. |
| 4/21 | Lecture 9 |
Propreties of the integral.
Homework 3 due. |
| 4/24 | Lecture 10 | Integration and differentiation. |
| 4/26 | Lecture 11 |
Midterm 1. |
| 4/28 | Lecture 12 | Further properties of the integral |
| Chapter 7. Sequences and series of functions. | ||
| 5/1 | Lecture 13 | Sequences and series of functions. |
| 5/3 | Lecture 14 | Uniform convergence. |
| 5/5 | Lecture 15 |
Uniform convergence and continuity.
Homework 4 due. |
| 5/8 | Lecture 16 | Uniform convergence and integration. |
| 5/10 | Lecture 17 | Uniform convergence and differentiation. |
| 5/12 | Lecture 18 |
Equicontinuity.
Homework 5 due. |
| 5/15 | Lecture 19 | Equicontinuity and compactness. |
| 5/17 | Lecture 20 | Stone Weierstrass. |
| 5/19 | Lecture 21 | Midterm II |
| 5/22 | Lecture 22 |
Stone-Weierstrass |
| 5/24 | Lecture 23 | Stone-Weierstrass. |
| Chapter 8. Special functions. | ||
| 5/26 | Lecture 24 |
Power series.
Homework 6 due. |
| 5/31 | Lecture 25 | Exponential and logarithm. |
| 6/2 | Lecture 26 | Trigonometric functions. |
| 6/5 | Lecture 27 | Fourier Series. |
| 6/7 | Lecture 28 | Fourier Series. |
| 6/9 | Lecture 29 |
Fourier Series.
Homework 7 due. |
| 6/16 | Final Exam. |