Math 3001, Analysis 1
Semester 2, 2011-12
Course Lecturer
Dr. Judith Packer, Dept. of Mathematics
Tel: (303) 492-4989
Office: Math 266
Email: packer@colorado.edu
URL: http://spot.colorado.edu/~packer
Course Syllabus: For course syllabus, click here!
This course has a page at piazza.com - go to here and log in to see it.
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, or instructor consent.
Course Text:
We will use the text "Analysis, With an Introduction to Proof", S.R. Lay, Pearson - Prentice Hall, 2005,
4th edition. After a quick review of Chapters 1 and 2, we will cover most of Chapters 3--7, and part of Chapter 8.
Dr. Lay's web page has a link to an errata page for the 4th Edition at
http://webpages.leeu.edu/slay/
Assessment:
- Homework Assignments (every week): 20 %
- In-class mid-term exam - Wednesday, February 22, 12 p.m.- 1 p.m.: 25 %
- In-class mid-term exam - Wednesday, April 4, 12 p.m. - 1 p.m. 25 %
- In-class final exam, Wednesday, May 9, 4:30 p.m. -- 7:00 p.m. : 30 % .
Lecture Hours and Venue:
MWF 12 p.m.-12:50 p.m. RAMY N1B31.
Office Hours:
1 p.m. - 2 p.m., Math 266 MWF, and 3 p.m. - 4 p.m., Monday.
Some slides shown in class:
Homework:
- Assignment 1, now due Friday January 27: Sections 10, 11, problems 10.3, 10.4, 10.7, 10.14, 10.16, 10.20, 10.22, 11.4, 11.6, 11.7, 11.8, 11.10.
- Some solutions to HW 1.
- Assignment 2, due Friday, February 3: Read Sections 12, 13, do problems 12.3 (a), (d), (f), (h), (i), (k), (n), 12.7, 12.8, 12.12, 13.3, 13.4, 13.5, 13.8, 13.14. Extra credit: 13.15.
- Some solutions to HW 2.
- Assignment 3, due Friday, February 10: Review Section 13, begin reading Section 14, do problems 13.6, 13.9 (a), 13.10, 13.16,
13.20, 13.21 (a), (d), (e), 13.22.
- Some solutions to HW 3.
- Assignment 4, due Friday, February 17: Read Sections 16, 17, do problems
16.2, 16.6, 16.7, 16.9, 16.11, 16.12, 17.1, 17.5 (a), (b), (e), (g), (i), (j),
17.15 (b), (c).
- Some solutions to HW 4.
- Assignment 5, due Friday, March 2: Read Sections 18, 19, do problems 17.16, 18.1, 18.3 (a),(d), 18.7, 18.9, 18.10, 19.3, 19.4, 19.7, 19.11, 19.13.
- Some solutions to HW 5.
- Assignment 6, due Friday, March 9: Read Sections 20 and first half of 21, do problems 20.3 (a), (c), (d), (e), (h), 20.4, 20.9, 20.14, 20.16, 20.18, 21.4, 21.8. 21.10, 21.12, 21.13.
- Some solutions to HW 6.
- Assignment 7, due Friday, March 16: Read Sections 21, 22, and pp. 216-218 of 23; do problems 21.3, 21.14, 21.17, 21.18, 22.4, 22.6, 22.7, 22.8, 22.9, 22.12, 22.16,
23.4, 23.6.
- Some solutions to HW 7.
- Assignment 8, due Friday, March 23: Read rest of Section 23, and Section 25, do 23.5, 23.7, 23.11, 25.5, 25.8, 25.11, 25.12, 25.13, 25.14.
- Some solutions to HW 8.
- Assignment 9, due Friday, April 13: Read rest of Section 26, begin Section 29;
do 26.1, 26.3, 26.5 (a),(b),(f), 26.11, 26.13, 26.15, 26.17, 26.18, 29.4, 29.5, 29.8.
- Some solutions to HW 9.
- Assignment 10, due Friday, April 20: Finish reading Section 29, begin reading Section 30: do 29.11, 29.12, 29.13, 29.15, 29.16, 29.17, 30.3, 30.5, 30.6, 30.8, 30.9.
- Some solutions to HW 10.
- Assignment 11, due Friday, April 27: Finish reading Section 30, reading Section 31: do 30.11, 30.15, 30.17, 31.5, 31.11, 31.12, 31.14, 31.15, 31.16.
- Some solutions to HW 11.
- Extra Credit Assignment, due Friday May 3: can be used to replace score from any other assignment:
do problems on sample exam m4310f.pdf on piazza.com - Q 1(i), (ii), Q 2 (i),Q3
(i), (ii),
Q 5(i), Q 6 (i), (ii).
- Some solutions to Extra Credit Assignment.
Some Important Names associated with Analysis :
Back to the home page of Judith A. Packer
Last modified January 12
, 2012.