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 xhour instead of the class on Monday January 19 Final day for electing
use of the NonRecording 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 xhour 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 xhour 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 NonRecording
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 
StoneWeirstrass Theorem without proof, Wrap up J 