Spring Semester 2004-2005

MATH 3243: Advanced Calculus

MWF, 13:00-13:50, Room: Boyd Building 304

Textbook: Analysis: with an Introduction to Proof, Third Edition, by Steven R. Lay

Prentice Hall, Inc. 2001,  ISBN 0-13-089879-1

We will cover Chapters 3-7.

Instructor: Dr. Vu Kim Tuan                          Office: Boyd Building 325

Phone: 678-839-4135                                       E-mail: vu@westga.edu

Lecture Hours: MWF 1 PM-1:50 PM

Office Hours: Mondays 2 PM-3 PM, Wednesdays, 11:50 AM-1 PM, 2 PM-3 PM,  Fridays : 11:50 AM – 1 PM, or by appointment.

Course Description: This course is a rigorous introduction to the fundamental concepts of single-variable calculus. Topics include the real numbers, limits, continuity, uniform continuity, differentiation, integration, and sequences and series.

Learning Outcomes: the student will be able:

-To understand the concept of completeness of the system of real numbers: a least upper bound, a greatest lower bound.

-To understand the concept of topology of the reals: open sets, close sets, accumulation points, closure, open cover, compact sets.

-To understand the concept of convergence, and to use the notion of epsilon-delta correctly.

-To understand the concept of sequences and subsequences, monotone sequences and Cauchy sequences.

-To understand the concept of  one-sided limits, continuity and uniformly continuity.

-To understand the concept of derivative, l’Hospital’s rule, Taylor’s formula.

-To understand the concept of upper sum, lower sum, Riemann integrability.

-To prove main theorems of analysis of the real line: Heine-Borel theorem, Bolzano-Weierstrass theorem, Nested Interval theorem, Monotone Convergence theorem, Cauchy Convergence Criterion, Intermediate Value theorem, Chain Rule, Rolle’s theorem, Mean Value Theorem for Derivatives, Cauchy Mean Value theorem, , l’Hospital’s rule, Taylor’s theorem, Fundamental Theorems of Calculus.

Tests and Final Exam: There will be two in-class tests and two take-home tests worth 100 points each. Take-home tests are supposed to be completed individually. The lowest of these test scores will be dropped. You can miss at most one test, and that test will be considered to be the test with the lowest score to be dropped. The final counts 200 points.

Extra Credits: We are in process of organizing a Workshop on Sampling. Some leading experts will visit UWG to deliver lectures for students. The tentative dates for the workshop are March 11-12, 2005. You are encouraged to attend these lectures, and up to 25 bonus points will be given for the attendance. If the workshop does not take place in this semester, a bonus question worth 25 points will be added to the final examination.

Important Dates: 2/4 : Test 1 (In-class)    2/25  : Test 2 (Take-home)  Due 2/28

                               4/1 : Test 3 (In-class)    4/22  : Test 4 (Take-home)  Due 4/25       

                               Final: May 6, 11 AM – 1 PM

No class on January 17 (Martin Luther King Holiday), March 11 (in case the workshop takes place),  March 18 (Math Day), March 21-25 (Spring Recess),  March 30 (Honors Convocation)

Grading:  The final letter grade will be determined by the following scale:

A   = 450-525,     B   = 400-449,    C   = 350-399,    D   = 300-349,        F    = below  300

W Deadline: March 3rd is the last day to withdraw with grade W

Homework: This is an important part of the course. At the end of most classes you will be given a list of problems – these are the minimum that you should work. These problems will not be graded. Some of these problems will be gone over in the next class session and some will be included into the in-class tests. Practice is important. I encourage you to use my office hours if you have any questions about them. You should make sure to set aside some time every class day to work problems.

Disabilities:  Students with documented disabilities (through West Georgia’s Disability Services) will be given all reasonable accommodations.  Students must take the responsibility to make their disability known and request academic adjustments or auxiliary aids.  Adjustments needed in relation to test-taking must be brought to the instructor's attention well in advance of the test (at least one week prior).

Attendance Policy: You are expected to attend every class. Although absences are not penalized, if a class is missed, you are responsible for all material and assignments.

Academic Honesty:    You are expected to achieve and maintain the highest standards of academic honesty and excellence as described in the Undergraduate Catalog. In short, be responsible and do your own work.