Math 63 Winter 2009
Syllabus
This is a tentative syllabus. In all likelihood, one of the textbook chapters on this syllabus will actually be omitted. This page will be updated irregularly.
|
Date |
Sections |
Description |
|
Monday January 5 |
Chapter 1 |
Ordered sets, fields, the Real field |
|
Wednesday January 7 |
Chapter 1 |
Extended real number system, Complex field |
|
Friday January 9 |
Finish Chapter 1 and start Chapter 2 |
Euclidean Spaces; Finite, countable and uncountable sets |
|
Monday January 12 |
Chapter 2 |
Metric spaces and compact sets |
|
Wednesday January 14 |
Chapter 2 |
Perfect and connected sets |
|
Friday January 16 |
Chapter 3 |
Numerical sequences, convergent sequences, subsequences |
|
Monday January 19 Martin Luther King Jr.
Day. No class |
|
|
|
Tuesday January 20 x-hour instead of the class on Monday January 19 Final day for electing
use of the Non-Recording option |
Chapter 3 |
Cauchy sequences |
|
Wednesday January 21 |
Chapter 4 |
Upper and lower limits; some special sequences |
|
Friday January 23 |
Chapter 4 |
Series, nonnegative term series |
|
Monday January 26 |
Chapter 4 |
Number e, the root and the ratio test |
|
Wednesday January 28 |
Chapter 4 |
Power series, alternating series, absolute convergence |
|
Friday January 30 The takehome Midterm exam is
given out. It will be due on Wednesday February 4 |
Chapter 4 |
Addition and multiplication of series, rearrangements |
|
Monday February 2 |
Chapter 5 |
Limits of functions and continuous functions |
|
Wednesday February 4 The Midterm Exam is due |
Chapter 5 |
Continuous functions on compact sets |
|
Friday February 6 |
Chapter 5 |
Intermediate value theorems, various types of discontinuities |
|
Monday February 9 |
Chapter 5 |
Monotonic functions and limits involving infinity |
|
Tuesday February 10 x-hour instead of the class on Friday February 13 |
Chapter 5 |
Derivative of a function of one variable, behavior of the derivative under elementary operations on functions |
|
Wednesday February 11 |
Chapter 5 |
Mean value theorem, L’Hopital’s rule |
|
Friday Feburary 13 Winter Carnival! No class J Final day for
dropping a fourth course without a grade notation of "W" |
|
|
|
Monday February 16 |
Chapter 5 |
Higher order derivatives, |
|
Wednesday February 18 |
Chapter 6 |
Riemann integral, partitions, refinements; important classes of integrable functions |
|
Friday February 20 |
Chapter 6 |
More of the important classes of integrable functions, properties of the integral |
|
Monday February 23 |
Chapter 6 |
Change of variables under integration |
|
Tuesday February 24 x-hour The last day to withdraw from a course |
Chapter 6 |
Integration by parts and the Fundamental Theorem of Calculus |
|
Wednesday February 25 |
Chapter 6 |
Wrap up integration |
|
Friday February 27 |
Chapter 7 |
Series and sequences of functions, examples, uniform convergence |
|
Monday March 2 Note that Tuesday
March 3 is the final day to alter grade limit filed under the Non-Recording
Option |
Chapter 7 |
Uniform convergence and continuity |
|
Wednesday March 4 |
Chapter 7 |
Uniform convergence, differentiation and (if we have time) integration. |
|
Friday March 6 |
Chapter 7 |
Finish uniform convergence and integration, equicontinuous families of functions |
|
Monday March 9 The take home Final Exam will be distributed on this day. It will be due on Saturday March 14 |
Chapter 7 |
Stone-Weirstrass Theorem without proof, Wrap up J |