| Instructor: | Jonathan White |
| E-Mail: | JWhite@Coe.Edu |
| Web Page: | http://www.coe.edu/~jwhite/ |
| Office: | Hickok 206A |
| Office Hours: | 10:00-10:50 MWF, 3:00-3:50 MTW, and by appointment |
| Office Phone: | 399-8280 |
| Home Phone: | 841-5111 (between 7am and 11pm) |
| Text: | Introductory Mathematical Analysis, by Witold Kosmala, Wm. C. Brown Pub |
| Problem Sets: | Problem Sets will be given throughout the term to supplement class work. Combined these will be worth 200 points (33.3% of the final grade). |
| Exams: | There will be two exams during the course of the semester, administered
during class time. The dates of these are indicated in the schedule on
the back side of this sheet. These exams will be worth 100 points (16.7%
of the final grade) each.
The final exam will be given Wednesday, December 11th, and will be worth 200 points (33.3% of the final grade). |
| Grading: | Grading will approximately follow a 90% A, 80% B, 70% C, 60% D scale. |
"And what are these fluxions? The velocities of evanescent increments. And what are these same evanescent increments? They are neither finite quantities, nor quantities infinitely small, nor yet nothing. May we not call them ghosts of departed quantities?"
-Bishop George Berkeley, 1685-1753
Real Analysis is in many ways a dramatically different course than anything
which preceeds it in the mathematics curriculum. In some regards, students
finally get a chance to see the sorts of things that professional mathematicians
deal with -- but at the same time, many of these underpinnings are beneath
notice once they've been properly laid. The simplest thing that can safely
be said is that there are genuinely troubling issues left unaddressed by
the undergraduate calculus sequence, and they must be dealt with before
moving on.
It is also important to note at this point that the demands on students become qualitatively different in this course than in its prerequisites. Learning strategies which have succeeded in previous classes will not necessarily suffice at this level. If at some point these challenges or frustrations get too bad, I strongly encourage you to see me for extra explanation -- don't wait until you're overwhelmed. I'm here to help.
Tentative Schedule
|
§1.1 Sets |
§1.2 Relations |
§1.3 Induction |
|
No Class -- Labor Day |
§1.4 Countability |
§1.5 Proofs |
|
§1.6 Real Numbers |
§1.7 Real Number Properties |
§1.8 Review |
|
§2.1 Convergence |
§2.2 Limit Theorems |
§2.3 Infinite Limits |
|
§2.4 Monotone Sequences |
§2.5 Cauchy Sequences |
§2.6 Subsequences |
|
§2.7 Review |
Review for Exam |
Exam 1 |
|
§3.1 Limit at Infinity |
§3.2 Limit at a Real Number |
§3.2 Limit at a Real Number |
|
No Class -- Fall Break |
§3.3 One-Sided Limits |
§3.4 Review |
|
§4.1 Continuity |
§4.2 Discontinuity |
§4.3 Properties of Cont. Func. |
|
§4.4 Uniform Continuity |
§4.5 Review |
§5.1 Derivatives |
|
§5.2 Properties of Derivatives |
§5.2 Properties of Derivatives |
§5.3 One-sided Derivatives |
|
§5.4 Higher Derivatives |
No Class -- Registration |
§5.5 Fixed Points |
|
§5.6 L'Hôpital's Rules |
§5.7 Review |
Review for Exam |
|
Exam 2 |
No Class -- Thanksgiving |
No Class -- Thanksgiving |
|
§6.1 Riemann Integral |
§6.2 Integrable Functions |
Review for Final |
|
Final Exam |
||
Any student in this course who has a disability that may prevent him or her from fully demonstrating his or her abilities should contact me personally as soon as possible so that we can discuss accommodations necessary to ensure full participation and facilitate your educational opportunities.