The main page of the course (go there for announcements and links).
TIME/PLACE: MWF 12-12:50, Altgeld 243.
INSTRUCTOR:
Timur Oikhberg
e-mail:
oikhberg@illinois.edu
Office: Illini Hall 340.
Telephone: (217) 265-6312.
URL:
http://www.math.uiuc.edu/~oikhberg/F08/444/ea.html
OFFICE HOURS:
MW 3:15 - 4:45, or by appointment.
COURSE DESCRIPTION: This course is an introduction to epsilon-delta analysis on the real line for students who do not plan graduate study in mathematics (those students should take MATH 447).
PREREQUISITES: MATH 241; MATH 347 or MATH 348, or equivalent courses.
TEXT:
R. B. Bartle and D. R. Sherbert, Introduction to Real Analysis,
3rd Edition, John Wiley & Sons, 2000.
Be prepared to take comprehensive lecture notes.
The information discussed in class will be part of the examination material.
Extra reading: many books are available to those who are interested
in Real Analysis. I can recommend the classics: Real Analysis, by
H. L. Royden, or Real and Comples Analysis, by
W. Rudin.
TENTATIVE COURSE SCHEDULE:
| Chapter | Topics and sections | Class hours |
| 1 | Preliminaries
We will treat Sections 1.1, 1.2 lightly, concentrating on Section 1.3. |
3 |
| 2 | The Real Numbers
Sections 2.1, 2.2 will be covered quickly, with emphasis placed on 2.3 and 2.4. We may omit the discussion of decimals in Sec. 2.5. |
5 |
| 3 | Sequences
We may omit Section 3.6. |
9 |
| 4 | Limits
We will omit Section 4.3 |
3 |
| 5 | Continuous Functions
We will omit Sections 5.5, 5.6, and may omit polynomial approximation in Section 5.4 (pp. 140-144) |
6 |
| 6 | Differentiation
We will omit Sections 6.3, 6.4. |
3 |
| 7 | The Riemann Integral
We will omit Section 7.4 |
6 |
| 8 | Sequences of Functions
Time permitting, we will cover 8.1 and as much of 8.2 as possible |
TESTS: There will be two midterm tests: on Wednesday, October 8, and Wednesday, November 19. The comprehensive final exam will be given on Wednesday, December 17, 1:30-4:30 PM, in our classroom. Only students with University-approved excuses (illness, death in the family, religious observances, or conflicts as defined by the University policies) will be allowed to take make-up tests. Please bring your student ID to all tests.
HOMEWORK: Homework assignments will be given and collected according to the following schedule:
| No. | Assigned by | Collected on |
| 1 | Friday 08/29 | Friday 09/05 |
| 2 | Friday 09/05 | Friday 09/12 |
| 3 | Friday 09/12 | Friday 09/19 |
| 4 | Friday 09/19 | Friday 09/26 |
| 5 | Friday 09/26 | Friday 10/03 |
| 6 | Friday 10/03 | Friday 10/17 |
| 7 | Friday 10/17 | Friday 10/24 |
| 8 | Friday 10/24 | Friday 10/31 |
| 9 | Friday 10/31 | Friday 11/07 |
| 10 | Friday 11/07 | Friday 11/14 |
| 11 | Friday 11/21 | Wednesday 12/03 |
| 12 | Wednesday 12/03 | Wednesday 12/10 |
Homework assignments are to be turned in at the beginning
of the class. Late homeworks will not be accepted.
The two weakest homework scores will be dropped. Only the 10 best
scores will be used to compute the grade for the course.
Homework Rules: (1) Print your name and course number at the top of the paper.
(2) Staple the papers together if your homework takes more than one page.
(3) Work out the problems, and justify your answers. (4) Be sure your homework
is neat and legible.
Grading: Not all homework problems will be given the same weigth.
Some problems may not be graded at all.
Bonus problems will be included in some homework assignments.
COURSE FORMAT: Most of the class meetings will be lectures. Usually, part of the class preceding an assignment submission date will be devoted to a discussion on the homework problems. For instance: we will discuss problems from Homework 1 (due Friday, Sep. 5) on Wednesday, Sep. 3. There will be reviews before tests. Check the class log for more information.
GRADES ON-LINE: The grades will be posted at Score Reports (https://www-s.math.uiuc.edu/bluestem/grades.cgi), which is the Math Department's gradebook program. This service will be available beginning approximately two weeks into the semester. You will be prompted for your NetID and NetID password after following the Score Reports link. Please check score reports regularly to make sure your grades have been correctly reported and tell me promptly about any errors. Please keep all of your graded homework and exams so that any discrepancies in recorded grades can be settled.
GRADING:
Components:
Homeworks: 10 x 3%.
Midterms: 2 x 20%.
Final: 30%.
Guidelines:
A - 90%, B - 75%,
C - 60%, D - 45%.
ACADEMIC DISHONESTY: Please review the academic integrity policies at http://www.admin.uiuc.edu/policy/code/article_1/a1_1-401.html. Cheating or plagiarism may result in a failing grade.
UNIVERSITY RESOURSES: Among many resourses, two need to be mentioned: