Department
Home Page
About Us:
• Contact Info.
• Faculty
• Staff
• Students
Academic Program:
• Admission
• Undergraduate
• Graduate
• Certificates
Courses:
• Course Description
• Class Web Pages
• Class Syllabi
•
Skills Tests
Research:
• Research Groups
• Colloquium
• Seminars
Links:
|
Phone: (407) 823-6284;
Fax: (407) 823-6253; MAP 207
MAA
5210
.01
Topics in Advanced Calculus
Fall
2002
, 4
credit hours
| | INSTRUCTOR | Dr.
Arthur A. Danielyan
| | OFFICE | MAP 124
| | OFFICE HOURS | 2:00-3:00p.m. MTWF, 6:00-7:00 W
and by appointment
| | PHONE | 823-4310
| | EMAIL | adaniely@pegasus.cc.ucf.edu
| | CLASS LOCATION | MAP 108
| | CLASS TIMES | 7:00-8:45p.m. MW
| | TEXTBOOK | Advanced Calculus, 3rd ed., 1983
| | by | Angus E. Taylor and W. Robert Mann
|
HOMEWORK
Selected homework problems will be collected and graded.
|
TESTS
There will be two tests and a final. Test 1 - MONDAY, SEPTEMBER 30; Test 2 - MONDAY, NOVEMBER 4; Final - WEDNESDAY, DECEMBER 4.
|
GRADING POLICY
The grade will be out of 100% made up from contributions from the following sources: 2 tests - 40% (i.e. 20% each), final - 40%, homework - 20%.
|
GRADING SCALE |
| Average | Grade | | 90 - 100%
| A | | 80 - 89%
| B | | 70 - 79%
| C | | 60 - 69%
| D | | 0 - 59%
| F | |
IMPORTANT DATES
Withdrawal Deadline - October 11.
|
TENTATIVE LIST OF TOPICS
The real number system (review; sec. 2.4-2.8).
Limit superior and inferior (21.5).
Euclidean n-spaces (R^n), open and closed sets in R and R^n, (sec. 5.1; 16.2-16.4), Bolzano-Weierstrass theorem in R and R^n (16.3-16.4), Sequential limits in R and R^n (1.62; 16.41), Compactness, Heine-Borel theorem in R and R^n (16.6), Relative topology, Connectedness in R^n (17.7), Limits and continuity in R^n (5.2, 17.1-17.7), Uniform continuity and the uniform norm (17.4).
Riemann integration (18.1-18.5), Riemann's condition for integrability (18.1), The Fundamental Theorem (18.4-18.41), Uniform convergence and integrals.
Differentiation in R^n; differentiability (7.1-7.2; 11.8-11.10; 12.1-12.21; 12.5), The chain rule in R^n (6.5, 9.3), The mean value theorem in R^n (7.4), Taylor's theorem in R^n (7.5), Jacobians (6.6; 9.6; 12.2), Implicit and inverse function theorems (8.1; 8.2; 9.1; 12.6-12.7), Multiple integrals (18.6-18.8), Change of variables theorem (15.32, 15.62).
|
OTHER INFORMATION
PREREQUISITE: Advanced Calculus 1 (MAA 4226) or equivalent.
Knowledge of Advanced Calculus 1 (MAA 4226), or its equivalent is necessary for successful study in this course.
|
CLASS WEB PAGE
|
|
