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MATH 140B: Foundations of Real Analysis
Spring 2013

SYLLABUS

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.