Spring 2002, Math 104

April and May

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

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

Due Monday 4/1 at 8am

Q & A for Exam 2

• To read: Review Sections 9.1, 8.2-8.3, 10.1-10.2, 10.4. 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:

• New Time! If you have questions on the HW, Rachel is available at 6:30 Sunday evenings to help you. e-mail her at rzeigowe before 4 on Sunday.
• Bring remaining questions on PS 8 to class on Monday. You will not turn it in, but it is covered on the exam.
• The deadline to get 80% on the antidifferentiation exam is Monday at 3pm. After that, you have until April 22nd to get 50%.
• 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.

Due Wednesday 4/3 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 4/3

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, . . .

Reminders:

• Look at PS 9.
• If you plan on coming to my office hours Wednesday night, please e-mail me by 5pm, so I know to be here!

Due Friday 4/5 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 4/5

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?

Reminder:

• Stop by my office hours and clear up those misunderstandings! We're starting some fairly abstract stuff, and we want to make sure you get it as deeply as possible.

Due Monday 4/8 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 4/8

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)

Reminders:

• New Time! If you have questions on the HW, Rachel is available at 6:30 Sunday evenings to help you. e-mail her at rzeigowe before 4 on Sunday.
• Bring remaining questions on PS 9 to class on Monday.

Due Wednesday 4/10 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 4/10

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

Reminders:

• Look at PS 10 on the course web page.
• If you plan on coming to my office hours Wednesday night, please e-mail me by 5pm, so I know to be here!

Due Friday 4/12 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 4/12

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

Reminders:

• Keep on working hard and coming to my office hours!

Due Monday 4/15 at 8am

Project 3

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

Reminders:

• New Time! If you have questions on the HW, Rachel is available at 6:30 Sunday evenings to help you. e-mail her at rzeigowe before 4 on Sunday.
• Bring remaining questions on PS 10 to class on Monday.
• Remember the group problem set mantra: switch authors, label author, photocopy.

Due Wednesday 4/17 at 8am

The Big Picture

• Be sure to understand: The difference between a sequence and a series; what a partial sum really is and how it relates to the original series; the convergence tests.

Reminders:

• Look at PS 11 on the course web page.
• If you plan on coming to my office hours Wednesday night, please e-mail me by 5pm, so I know to be here!
• Exam 3 is next Tuesday. Make a study plan, and as usual give yourself at least 8 hours -- more if you're finding this material tricky. Because this material is more abstract than we've been dealing with, you want to be sure to spread your study time out over several days -- cramming is even more of a bad idea than usual!

Due Friday 4/19 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 4/19

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:

• Start studying for Exam 3, if you haven't already.
• Come to me with your questions!

Due Monday 4/22 at 8am

Q & A for Exam 3

• To read: Review Sections 11.1, 11.2, 11.3. Do the study guide. Redo problems from past problem sets.
• Be sure to understand: Everything, better than you did the first time around.

Reminder:

• New Time! If you have questions on the HW, Rachel is available at 6:30 Sunday evenings to help you. e-mail her at rzeigowe before 4 on Sunday.
• Bring remaining questions on PS 11 to class on Monday.
• Exam 3 is Tuesday, 4/23 in lab. As always, you may begin taking it at 12:30, and you should bring a calculator and your "cheat sheet", which meets the same specifications as before: handwritten by you, front only, standard sized paper.

Due Wednesday 4/24 at 8am

Section 11.4: Absolute Convergence: Alternating Series (cont)

• Be sure to understand:

E-mail Subject Line: Math 104 Your Name 4/24

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

Reminder:

• Look at PS 12.
• If you plan on coming to my office hours Wednesday night, please e-mail me by 5pm, so I know to be here!
• Keep working on the project.

Due Friday 4/26 at 8am

Section 11.4: Absolute convergence: Alternating Series (continued)

• To read: Re-read the section again, now that you (hopefully) really get Sections 11.1-11.3.

Reminder:

• Surely you have questions, so come on by my office hours!

Due Monday 4/26 at 8am

Section 11.5: Power Series

• Be sure to understand: Examples 4 and 6

E-mail Subject Line: Math 104 Your Name 4/29

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:

• New Time! If you have questions on the HW, Rachel is available at 6:30 Sunday evenings to help you. e-mail her at rzeigowe before 4 on Sunday.
• Bring remaining questions on PS 12 to class on Monday.
• Finish your calculations on the project by Monday (remember to consider the more general question you were asked!). Bring a rough draft in for me to look at Tuesday or Wednesday.

Due Wednesday 5/1 at 8am

11.6: Power Series as Functions

• To read: All of it by Tuesday! Re-read it for Wednesday.
• Be sure to understand: Example 3

E-mail Subject Line: Math 104 Your Name 5/1

1. Give two good reasons for writing a known function ( such as cos(x) ) as a power series.
2. Write cos(2x) as a power series.

Reminder:

• Bring a rough draft for me to look at by Wednesday.
• If you plan on coming to my office hours Wednesday night, please e-mail me by 5pm, so I know to be here!

Due Friday 5/3 at 8am

11.6: Power Series as Functions

• Be sure to understand: Example 3

E-mail Subject Line: Math 104 Your Name 5/3

1. Find the elementary function represented by the power series
sum(k*xk-1,k=1..infinity)
by manipulating a more familiar power series.

Reminder:

• Project 3 is due Friday by 2pm.
• The take-home portion of your final is due Monday May 6 at 2pm; the in class will be Monday from 2-5pm.

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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