Fall 2000, Math 104

November

Be sure to check back often, because assignments may change!

All section and page numbers refer to sections from Ostebee/Zorn, Vol 2.

Wednesday 11/1 at 8am

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.

E-mail Subject Line: Math 104 Your Name 11/1

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 ak of the sequence
1, -2, 4, -8, 16, -32, . . .

Reminder:

• PS 8 (group) is due Wednesday.
• Look at PS 9.
• If you have last lingering questions, and would like some additional help, come to my office hours (of course, or e-mail Annie by 5pm Tuesday (at amachaff) to let her know you'd like to meet with her Tuesday at 8pm in A102.
• Your project is due Wednesday. Bring in a rough draft before hand, and have a friend who is not in this class (and preferably, who is not familiar with Calc 2) read through your letter to see if they can understand the situation, and if they find your solution convincing, not confusing, and not too dry.
• Get a start on studying for that exam!

Due Friday 11/3 at 8am

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

E-mail Subject Line: Math 104 Your Name 11/3

1. There are two sequences associated with every series. What are they?
2. Does the geometric series
sum( ' (1/4)k ', k=0 .. infinity)
converge or diverge? Why?

Reminders:

• The deadline to get any credit at all on the antidifferentiation exam is Monday 11/6. If you have not passed it yet, but pass it by Monday at 4pm, you will get 50%. Otherwise, you will get a 0%. Please don't make me give you a 0 :(

Due Monday 11/6 at 8am

Q & A for Exam 2

• To read: Review Sections 9.1, 8.2-8.3, 10.1-10.2, 11.1. Work on the study guide I gave you. Redo old problem sets.
• Be sure to understand: Everything better than you did the first time you saw it.

Reminders:

• Bring questions on PS 9 to class Monday.
• As before, you may have a "cheat sheet" for the exam Tuesday. It must follow the same guidelines as before: handwritten by you, no photocopying, on the front side of a piece of paper that is 8 1/2 x 11 or smaller only.
• You may begin taking the exam at 12:30pm on Tuesday. Don't forget to bring your calculator and your "cheat sheet" .
• Vote on Tuesday!

Due Wednesday 11/8 at 8am

Section 11.2: Infinite Series, Convergence, and Divergence

• To read: Finish this section, although you can de-emphasize the part on Telescoping Sums
• Be sure to understand: The nth Term Test

E-mail Subject Line: Math 104 Your Name 11/8

What does the nth Term Test tell you about each series? Explain.
1. sum('sin(k)', k=0..infinity)
2. sum('1/k ', k=0..infinity)

Reminder:

• PS 9 (ind) is due Wednesday.
• If you want some additional help, e-mail Annie before 5pm Tuesday about meeting with her at 8pm Tuesday.
• Look at PS 10 on the course web page.

Due Friday 11/10 at 8am

11.3: Testing for Convergence: Estimating Limits

• To read: Through page 577
• Be sure to understand: The statement of the Comparison Test

E-mail Subject Line: Math 104 Your Name 11/10

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

Reminders:

• Remember that I'm requiring you to attend the 1st Annual Norman Johnson lecture in Mathematics, Monday night at 7:30.

Due Monday 11/13 at 8am

Section 11.3: Testing for Convergence: Estimating Limits

• To read: Finish this section
• Be sure to understand: The statements of the Integral and Ratio Tests

E-mail Subject Line: Math 104 Your Name 11/13

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

Reminders:

• Bring questions on PS 10 (group) to class on Monday.
• The 1st Annual Norman Johnson lecture in Mathematics is tonight at 7:30. It is given by Tom Banchoff, and should be great. This lecture is a required part of this class. (I'll be there, making black marks against the names of those who do not come).

Due Wednesday 11/15 at 8am

Section 11.4 Absolute Convergence: Alternating Series

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

E-mail Subject Line: Math 104 Your Name 11/15

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

Reminders:

• PS 10 (gp) is due Wednesday. If you have any lingering questions, remember to contact Annie at amachaff before 5pm Tuesday about meeting with her at 8pm Tuesday in A102.
• Look at PS 11 on the course web page.

Due Friday 11/17 at 8am

Section 11.4: Absolute Convergence: Alternating Series (cont)

• Be sure to understand:

E-mail Subject Line: Math 104 Your Name 11/17

1. How close does S100 approximate the series
sum( ' (-1)k (1/k)', k=0 .. infinity) ?
Why?

Due Monday 11/20 at 8am

Section 11.5: Power Series

• Be sure to understand: Examples 4 and 6

E-mail Subject Line: Math 104 Your Name 11/20

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.

Reminder:

• Bring questions on PS 11 to class Monday.
• PS 11 is due Tuesday by 4pm.
• Take a quick look at PS 12 before you leave town for Thanksgiving!

Due Monday 11/27 at 8am

11.5: Power Series

• Be sure to understand: Everything

E-mail Subject Line: Math 104 Your Name 11/27

1. Find the radius and interval of convergence of the power series
sum((3x)n/n,n=1..infinity)
Reminders:
• Bring questions on PS 12 to class Monday.
• Read Project 3, which I will hand out in class Monday, before lab Tuesday!!
• Again, we have a project then an exam. Exam 3 is Tuesday 12/5. Start planning how you're going to study for the exam and work on the project!

Due Wednesday 11/29 at 8am

Project 3

• Be sure to understand: What your client is asking you to do!

Reminders:

• PS 12 (group) is due Wednesday.
• Look at PS 13.
• As always, bring your questions to me, and/or contact Annie (at amachaff) before 5pm Tuesday about meeting with her Tuesday at 8pm in A102.

Janice Sklensky
Wheaton College
Department of Mathematics and Computer Science
Science Center, Room 109
Norton, Massachusetts 02766-0930
TEL (508) 286-3973
FAX (508) 285-8278
jsklensk@wheatonma.edu

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