|
|
| MATH 215
MATHEMATICAL ANALYSIS SYLLABUS |
|
|
|
|
| Semester: |
Spring 2014 |
|
|
| Instructor: |
Mefharet Kocatepe |
|
|
| Office: |
Faculty of Science, Block A, Room: 115 A |
|
Phone: 1255 |
|
e-mail: kocatepe@fen.bilkent.edu.tr |
|
|
| Exams, grading: |
Midterm 1 (25%) March 14, 10:30-12:20 |
|
Midterm 2 (25%) April 25, 10:30-12:20 |
|
Final (30%) to be announced later |
|
Homework (20%) Ten homework assisgnments |
|
|
| Course Schedule: |
Wednesday 08:30-10:20 in EB-204 |
|
Friday 10:30-12:20 in EB-204 |
|
|
| Office hours: |
By appointment |
|
|
| Textbooks |
M. Rosenlicht, Introduction to Analysis, 1986, Dover |
|
W. Rudin, Principles of Mathematical Analysis, 3rd.
Ed., 2000, Wiley |
|
|
|
60% attendance is
required |
|
|
|
|
| Date |
Subjects |
| Feb.5, 7 |
Sets and functions |
| Feb. 12, 14 |
The real number system. |
| Feb. 19, 21 |
Metric spaces: definition
and examples |
| Feb. 26, 28 |
Topology of metric spaces |
| Mar. 5, 7 |
Sequences, Cauchy sequences
|
| Mar. 12, 14 |
Completeness, Midterm 1 |
| Mar. 19, 21 |
Completeness, Compact sets |
| Mar. 26, 28 |
Compact
sets |
| Apr. 2, 4 |
Connected
sets |
| Apr. 9, 11 |
Continuity |
| Apr.16, 18 |
Uniform
continuity |
| Apr. 25 |
Midterm 2 |
| April 30 |
Preservation of compactness and connectedness under continuity |
| May
7, 9 |
Contractions and Banach fixed point theorem |
| May
14, 16 |
Review |