MATH 3243 – Advanced Calculus
Section 01, Spring 2007
MWF 11:15 am – 12:10 pm 304 Boyd Bldg
Prerequisites: Math 3003.
Instructor: Dr. Rui Xu
Office: 311 Boyd Bldg
Phone: (678)839-4122
E-mail: xu@westga.edu
Website: http://www.westga.edu/˜xu/
Office hours: MF: 8:30 am – 10:00 am; 12:30 pm –2:30 pm; Wednesday: 8:30 am – 9:00 am;
12:30 pm –2:30 pm; Thursday: 10:30 am –11:00 am or by appointment.
Textbook: Analysis: With an Introduction to Proof (4th Edition) by Steven R. Lay. Prentice
Hall,Inc. 2004, ISBN 0-13-148101-0
Course Description: This course is a rigorous introduction to the fundamental concepts of
single-variable calculus. Topics include Logic and Proof, Sets and Functions, the real numbers,
limits, continuity, uniform continuity, differentiation, integration, and sequences and series.
Learning Outcomes: The student will be able to:
1. Understand the concept of completeness of the system of real numbers: a least upper
bound, a greatest lower bound.
2. Understand the concept of topology of the reals: open sets, close sets, accumulation points,
closure, open cover, compact sets.
3. Understand the concept of convergence, and to use the notion of epsilon-delta correctly..
4. Understand the concept of sequences and subsequences, monotone sequences and Cauchy
sequences..
5. Understand the concept of one-sided limits, continuity and uniformly continuity.
6. Understand the concept of derivative, l’Hospital’s rule, Taylor’s formula.
7. Understand the concept of upper sum, lower sum, Riemann integrability.
8. Prove main theorems of analysis of the real line: Heine-Borel theorem, Bolzano-Weierstrass
theorem, Nested Interval theorem, Monotone Convergence theorem, Cauchy Convergence Crite-
rion, Intermediate Value theorem, Chain Rule, Rolle’s theorem, Mean Value Theorem for Deriva-
tives, Cauchy Mean Value theorem, l’Hospital’s rule, Taylor’s theorem, Fundamental Theorems
of Calculus.
Grading Methods: Grades will be assessed based on a total of 500 points (as shown below),
using the standard decade scale: (90–100%=A, 80–89%=B, 70–79%=C , 60–69%=D, below
60%=F).
Test 1 (Jan. 31st) 100pts
Test 2 (Feb. 20) 100pts
Test 3 (March 28) 100pts
Test 4 (April 20) 100pts
Final (Comprehensive) 180pts
Attendance 20pts
Total 500pts (drop the lowest test score)
