Math 63 Winter 2009


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.

Math 63Main page





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, LíHopitalís 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, Taylorís theorem, and if we have time derivatives of complex-valued functions

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


The last day to withdraw from a course

Chapter 6

Integration by partsand 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