Fall 2007, Math 104

November and December, 2007

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

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

Due Friday 11/2 at 9am

Section 11.2 Infinite Series, Convergence, and Divergence

• To read: Finish the section (you should have started it for Thursday's class). Re-read through Example 4.
• Be sure to understand: The sections Why series matter: A look ahead and Definitions and terminology. The nth term test.

E-mail Subject Line: Math 104 Your Name 11/2

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?
3. What does the nth Term Test tell you about each series? Explain.

(a) sum(sin(k), k=0..infinity)
(b) sum(1/k , k=1..infinity)

Reminders:
• Begin PS 10.

Due Monday 11/5 at 9am

Section 11.2: Infinite Series: Convergence and Divergence

• To read: Re-read the whole section one more time -- really work to make sense out of everything.

Due Wednesday 11/7 at 9am

Section 11.3: Testing for Convergence; Estimating Limits

• To read: Through the section on the Integral test.
• Be sure to understand: How to use the comparison and integral tests to determine convergence; how to use them to estimate the accuracy of an approximation.

E-mail Subject Line: Math 104 Your Name 11/7

1. Explain in a couple of sentences why the Comparison Test makes sense.
2. Explain in a couple sentences why the Integral Test makes sense.

Reminders:

• Bring questions on PS 10

Due Friday 11/9 at 9am

Begin Working on Project 1

Reminders:

• Begin PS 11

Due Monday 11/12 at 9am

Continue Working on Project 2

Due Wednesday 11/14 at 9am

Section 11.3 Testing for Convergence; Estimating Limits

1. To read: Finish the section.
2. Be sure to understand: How to use the ratio test to determine convergence and divergence.

E-mail Subject Line: Math 104 Your Name 11/14

1. Explain in a couple of sentences why the Ratio Test makes sense.
Reminders:
• You should have the mathematics behind project 2 solved by Wednesday evening, so you can begin writing your response. I once again encourage you to bring me a draft.

Due Friday 11/16 at 9am

Section 11.4 Absolute Convergence; Alternating Series

• Be sure to understand: The statements of the Alternating Series test

E-mail Subject Line: Math 104 Your Name 11/16

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

Reminder:

• Begin PS 12

Due Monday 11/19 at 9am

Section 11.4 Absolute Convergence; Alternating Series

• Be sure to understand:

E-mail Subject Line: Math 104 Your Name 11/19

1. How closely does S100 approximate the series sum((-1)k (1/k), k=1 .. infinity) ? Why?
Reminder:
• Exam 3 is the Thursday after Thanksgiving break. While I know you are only just now finishing up Project 2, you may want to look at your post-break schedule and decide whether you want to get a good start on preparing yourself.

Due Wednesday 11/21 at 9am

Thanksgiving Break!

Due Friday 11/23 at 9am

Thanksgiving Break!

Due Monday 11/26 at 8am

Section 11.5 Power Series

• Be sure to understand: Examples 4 and 5.

E-mail Subject Line: Math 104 Your Name 11/26

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.

Due Wednesday 11/28 at 9am

Bring Questions for Exam 3

Reminders:

• PS 12 will not be collected, but it will be covered on the exam.
• As always, you may have handwritten notes on one side of a standard sheet of paper, and may begin the exam at 12:30.
• Get as many questions resolved before class on Wednesday as possible, through office hours and tutoring hours.

Due Friday 11/30 at 9am

Section 11.5 Power Series

• Be sure to understand: The whole thing!

Reminders:

• Begin PS 13

Due Monday 12/3 at 9am

Section 11.5 Power Series

• Be sure to understand: The whole thing!

Reminder:

• Do the rest of PS 12 and all of PS 13. Why? A take-home exam takes loads of time. You should always allot a minimum of all the time you'd ordinaraily spend studying (presumably an absolute minimum of 10 hours) plus the time you'd spend taking the exam (another 3 hours). The last thing you want to do is to skip doing one-and-a-half problem sets -- if you do, you can immediately add however long you usually spend working on 1 1/2 problem sets to the time you should allot to working on the exam!

(In my experience, most students do end up spending 20-25 hours on the final, but I suspect that's at least partly because many of them have not done the last couple sections worth of homework.)

Due Wednesday 12/5 at 9am

Section 11.6 Power Series as Functions
Section 11.7 Taylor Series

• To read: All of both sections
• Be sure to understand: The definition of a Taylor series

E-mail Subject Line: Math 104 Your Name 12/5

1. Give two good reasons for writing a known function ( such as cos(x) ) as a power series.
2. How does a Taylor series differ from a Taylor polynomial?
3. Why would you ever want to find the Taylor series of a function?

Reminder:

• Bring questions on Section 11.4 from PS 12 and on all of PS 13 to class Thursday.

Due Friday 12/7 at 9am

Section 11.7 Taylor Series

• Be sure to understand:

Here ends the reading for the Semester!

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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