Spring 2006, Math 104

April and May, 2006

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 Monday 4/3 at 9am

Section 11.2 Infinite Series, Convergence, and Divergence

• To read: Through Example 4. This can be tough going, but really work at it.
• Be sure to understand: The sections Why series matter: A look ahead and Definitions and terminology.

E-mail Subject Line: Math 104 Your Name 4/3

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:

• Take advantage of tutoring hours
• Bring questions on PS 9.

Due Wednessday 4/5 at 9am

Section 11.2: Infinite Series, Convergence, and Divergence

• Be sure to understand: The nth term test.

E-mail Subject Line: Math 104 Your Name 4/5

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

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

Reminders:

• Begin PS 10.

Due Friday 4/7 at 9am

Section 11.3: Testing for Convergence; Estimating Limits

• To read: Through the section on the Comparison test.
• Be sure to understand: How to use the comparison test to determine convergence; how to use it to estimate the accuracy of an approximation.

E-mail Subject Line: Math 104 Your Name 4/7

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

Due Monday 4/10 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 Integral test to determine convergence and divergence; how to use the Integral test to approximate to a desired accuracy.

E-mail Subject Line: Math 104 Your Name 4/10

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

Reminders:

• Bring questions on PS 10

Due Wednesday 4/12 at 9am

Re-read Section 11.3, through the Integral Test

Reminders:

• Begin PS 11

Due Friday 4/14 at 9am

Work on Project 2

Due Monday 4/17 at 9am

Continue working on Project 2

Reminders:

• Try to resolve as many of your homework questions as possible before coming to class Monday, so that you can maximize your project-working time. However, do bring unresolved questions to class on Monday: I may not go over them in as much detail as usual, but I'll give some hints.

Due Wednesday 4/19 at 9am

Section 11.3 Testing for Convergence; Estimating Limits

• Be sure to understand: How to use the comparison test and the integral test to find upper and lower bounds for a series, as well as to approximate a series.

Reminder:

• Begin PS 12

Due Friday 4/21 at 8am

Section 11.3 Testing for Convergence; Estimating Limits

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

E-mail Subject Line: Math 104 Your Name 4/21

1. Explain in a couple of sentences why the Ratio Test makes sense.
Reminder:
• You should have the mathematics behind project 2 solved by Friday, so you can begin writing your response. I once again encourage you to bring me a draft: If you bring it to me by Tuesday, I can spend some time on it and give you some specific comments; if you bring it later my suggestions will be more broad.

Due Monday 4/24 at 9 am

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 4/24

1. Give an example of a series that is conditionally convergent. Explain.
2. Give an example of a series that is absolutely convergent. Explain.
3. How closely does S100 approximate the series sum((-1)k (1/k), k=1 .. infinity) ? Why?

Reminders:

• Bring unresolved questions to class Monday.
• Continue working on wriiting up the project. Remember to use the writing guide and the checklist to help you.
• Exam 3 is Tuesday 5/2.

Due Wednesday 4/26 at 9am

Section 11.5 Power Series

• Be sure to understand: Examples 4 and 5.

E-mail Subject Line: Math 104 Your Name 4/26

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.
Reminders:
• Begin PS 13

Due Friday 4/28 at 9am

Section 11.5 Power Series

• Be sure to understand: The whole thing!

Due Monday 5/1 at 9am

Bring Questions for Exam 3

Reminders:

• PS 13 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 Monday as possible, through office hours and tutoring hours.

Due Wednesday 5/3 at 9am

Section 11.5 Power Series

• Be sure to understand: The whole thing!

Due Friday 5/5 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 5/5

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?

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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