Math 104 - Calculus II - Reading Assignments
November & December 2001

I'll use Maple syntax for mathematical notation on this page.
All numbers indicate sections from Ostebee/Zorn, Vol 2.

For November 2

Section 11.1 Sequences and Their Limits

• To read : Through page 557 and the statements of Theorem 2 and Theorem 3.
• Be sure to understand : The section of Fine Points on page 553, the statements of Theorems 2 and 3.

Email Subject Line : Math 104 11/2 Your Name

Reading Questions :

1. Does the following sequence converge or diverge? Be sure to explain your answer.
   1, 3, 5, 7, 9, 11, 13, . . .
2. Find a symbolic expression for the general term a_k of the sequence 1, 2, 4, 8, 16, 32, . . .

For November 5

Section 11.2 Infinite Series, Convergence, and Divergence

To read : Through Example 4. This can be tough going.

Be sure to understand : The section Series Language: Terms, Partial Sums, Tails, Convergence, Limit on page 563

Email Subject Line : Math 104 11/5 Your Name

Reading Questions :

1. There are two sequences associated with every series. What are they?
2. Does the geometric series (1/4)^k converge or diverge? Why?

For November 7

Section 11.2 Infinite Series, Convergence, and Divergence (cont)

To read : Finish this section, although you can de-emphasize the part on Telescoping Sums

Be sure to understand : The nth Term Test

Email Subject Line : Math 104 11/7 Your Name

Reading Questions : What does the nth Term Test tell you about each series? Explain.

1. 2^k
2. 1/k

For November 9

Section 11.3 Testing for Convergence: Estimating Limits

To read : Through page 577

Be sure to understand : The statement of the Comparison Test

Email Subject Line : Math 104 11/9 Your Name

Reading Question :

Explain in a couple of sentences why you think the Comparison Test should hold.

For November 12

Section 11.3 Testing for Convergence: Estimating Limits (cont)

To read : Finish this section

Be sure to understand : The statements of the Integral and Ratio Tests

Email Subject Line : Math 104 11/12 Your Name

Reading Question :

Explain in a couple of sentences why you think the Integral Test should hold.

For November 14

For November 16

Section 11.4 Absolute Convergence: Alternating Series

To read : All

Be sure to understand : The statement of the Alternating Series Test

Email Subject Line : Math 104 11/16 Your Name

Reading Questions :

1. Give an example of a series that is conditionally convergent. Explain.
2. Give an example of a series that is absolutely convergent. Explain.

For November 19

Section 11.4 Absolute Convergence: Alternating Series (cont)

To read : Re-read the section for today

Email Subject Line : Math 104 11/19 Your Name

Reading Question :

How close does S₁₀₀ approximate the series (-1)^k (1/k) ? Why?

For November 26

Section 11.5 Power Series

To read : All

Be sure to understand : Examples 4 and 6

Email Subject Line : Math 104 11/26 Your Name

Reading Questions :

1. How do power series differ from the series we have looked at up to this point?
2. What is the interval of convergence of a power series? Explain in your own words.

For November 28

Section 11.5 Power Series (cont)

To read : Reread this section

Be sure to understand : The section on "Power Series Convergence, Graphically"

Email Subject Line : Math 104 11/28 Your Name

Reading Questions :

1. Give an example of a power series with an interval of convergence of (-1/4, 1/4). Explain.
2. Give an example of a power series with an interval of convergence of (1, 3). Explain.

For November 30

Section 11.6 Power Series as Functions

To read : All

Be sure to understand : Example 3

Email Subject Line : Math 104 11/30 Your Name

Reading Question :

Give two good reasons for writing a known function ( such as cos(x) ) as a power series.

For December 3

Reread Section 11.6 for today. No reading questions due.

For December 5

Q & A for Exam 3 today. No Reading Assignment.

December 7 and 10

We will be reviewing the semester, so there are no specific new reading assignments.