## Math 3001, Analysis 1

## Semester 2, 2019-20

**Course Lecturer **
#### Dr. Judith Packer, Dept. of Mathematics

*Tel: (303) 492-6979*

Office: Math 227

Email: packer@colorado.edu

URL: http://math.colorado.edu/~packer

**Course Syllabus: For course syllabus, complete with list of university policies, click here! **

**LaTeX: Here is a link to information about the mathematical typewriting software LaTeX. ** This site has links to download sites, including
here .

**Course Information:**

This course is meant to familiarize the student with the rigorous theory behind the study of functions of a single real variable, and goes over the proofs of some of the
major results used in calculus. Topics to be covered include:
the topology and order structure of the real line; sequences of real numbers and limits of sequences; functions of a real variable:
limits of functions at a point, continuous functions and their properties -- Intermediate Value Theorem , uniform continuity;
the derivative of a function at a point and differentiability, the Mean Value Theorem, and
Taylor's Theorem; the Riemann integral and its properties, and the Fundamental Theorem of Calculus; and if time permits,
a brief overview of series of real numbers and power series expansions.

**Prerequisite:**

Math 2001 or the equivalent.

**Course Text:**

We will use the text "Analysis, With an Introduction to Proof", S.R. Lay, Pearson - Prentice Hall, 2014,
5th edition. After a quick review of Chapters 1 and 2, we will cover most of Chapters 3--7, and part of Chapter 8.

**Assessment:**
- Homework Assignments and in-class worksheets (every week): 25 %
- In-class mid-term exam - Wednesday, February 19, 10 a.m.- 11 a.m.: 25 %
- In-class mid-term exam - Friday, April 3, 10 a.m. - 11 a.m. 25 %
- In-class final exam, Saturday, May 2, 4:30 p.m. -- 7:00 p.m. : 25 % .
- Here is an example of a past year final exam.

**Lecture Hours and Venue: **

MWF 10 a.m.-10:50 a.m. ECCR 110.

**Office Hours: **

MWF 11 a.m. - 12 noon, and by appointment.

** Extra slides: **

** Homework: **

- Assignment 1: Due Wednesday, January 22: read Sections 3.1 and 3.2; do problems 3.1.3, 3.1.4, 3.1.7, 3.1.16,
3.1.20, 3.2.3 (a) (e) (j), 3.2.4, 3.2.6 all parts, 3.2.7, 3.2.8, 3.2.9.
- Assignment 2: Due Wenesday, January 29: read sections 3.3 and 3.4, do problems 3.3.3 (a), (d), (f), (h), (i), (k), (n),
3.3.7 (a), 3.3.8, 3.3.12 (a), (b), 3.4.3 (a), (c), (e), 3.4.4 (a), (c), (e), 3.4.5, 3.4.8, 3.4.14. For extra credit do 3.3.7 (b).
- Assignment 3, due Wednesday, February 5:
- Assignment 4, due Wednesday, February 12:
- Assignment 5, due Wednesday, February 26:
- Assignment 6, due Wednesday, March 4:
- Assignment 7, due Wednesday March 11:
- Assignment 8, due Wednesday, March 18:
- Assignment 9, due Wednesday April 1:
- Assignment 10, due Wednesday April 15:
- Assignment 11, due Wednesday April 22:
- Assignment 12, due Wednesday, April 29:
- Solutions to the Spring 2016 sample final exam.

**Some Important Names associated with Analysis :**

Back to the home page of Judith A. Packer

Last modified December 18, 2019.