Dates |
Lectures |
Topics |
Chapter 5. Differentiation. | ||
4/1 | Lecture 1 | Introduction. The derivative of a real function. |
4/3 | Lecture 2 | Derivatives and properties. Mean value theorems. |
4/5 | Lecture 3 | Continuity and derivatives. Intermediate value property. |
4/8 | Lecture 4 | L'Hopital's rule. Taylor's theorem. |
4/10 | Lecture 5 |
Vector valued functions. Homework 1 due. |
Chapter 6. Riemann Integral. | ||
4/12 | Lecture 6 | Definition of the integral. |
4/15 | Lecture 7 | Integration of continuous functions. |
4/17 | Lecture 8 |
Propreties of the integral.
Homework 2 due. |
4/19 | Lecture 9 | Propreties of the integral. |
4/22 | Lecture 10 | Integration and differentiation. |
4/24 | Lecture 11 |
Midterm 1. |
4/26 | Lecture 12 | Vector valued functions |
Chapter 7. Sequences and series of functions. | ||
4/29 | Lecture 13 | Sequences and series of functions. |
5/1 | Lecture 14 |
Uniform convergence.
Homework 3 due. |
5/3 | Lecture 15 | Uniform convergence and continuity. |
5/6 | Lecture 16 | Uniform convergence and integration. |
5/8 | Lecture 17 |
Uniform convergence and differentiation.
Homework 4 due. |
5/10 | Lecture 18 | Equicontinuity. |
5/13 | Lecture 19 | Equicontinuity and compactness. |
5/15 | Lecture 20 |
Stone-Weierstrass.
Homework 5 due. |
5/17 | Lecture 21 | Stone-Weierstrass. |
5/20 | Lecture 22 | Stone Weierstrass. |
5/22 | Lecture 23 |
Midterm 2 |
Chapter 8. Special functions. | ||
5/24 | Lecture 24 | Power series. |
5/27 | Memorial Day | No lecture. |
5/29 | Lecture 25 |
Exponential and logarithm.
Homework 6 due. |
5/31 | Lecture 26 | Trigonometric functions. |
6/3 | Lecture 27 | Fourier Series. |
6/5 | Lecture 28 |
Fourier Series.
Homework 7 due. |
6/7 | Lecture 29 | Fourier Series. |
6/14 | Final Exam. |