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.

Math 63Main page

 

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, 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

x-hour

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