**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*.- There are two sequences associated with every series. What are they?
- Does the geometric series sum((1/4)
^{k},k=0..infinity) converge or diverge? Why? - Take advantage of tutoring hours
- Bring questions on PS 9.
**To read:**Finish the section and reread through Example 4.**Be sure to understand:**The nth term test.- sum(sin(k), k=0..infinity)
- sum(1/k , k=1..infinity)
- Begin PS 10.
**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.- Explain in a couple of sentences why the Comparison Test makes sense.
**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.- Explain in a couple sentences why the Integral Test makes sense.
- Bring questions on PS 10
- Begin PS 11
- 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.
**To read:**Re-read through the integral test.**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.- Begin PS 12
**To read:**Finish the section.**Be sure to understand:**How to use the ratio test to determine convergence and divergence.- Explain in a couple of sentences why the Ratio Test makes sense.
- 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.
**To read:**All**Be sure to understand:**The statements of the Alternating Series test- Give an example of a series that is conditionally convergent. Explain.
- Give an example of a series that is absolutely convergent. Explain.
- How closely does S
_{100}approximate the series sum((-1)^{k}(1/k), k=1 .. infinity) ? Why? - 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.
**To read:**All**Be sure to understand:**Examples 4 and 5.- How do power series differ from the series we have looked at up to this point?
- What is the
**interval of convergence**of a power series? Explain in your own words. - Begin PS 13
**To read:**

Re-read this section**Be sure to understand:**The whole thing!- 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.
**To read:**

Re-read this section**Be sure to understand:**The whole thing!**To read:**All of both sections**Be sure to understand:**The definition of a Taylor series- Give two good reasons for writing a known function ( such as cos(x) ) as a power series.
- How does a Taylor series differ from a Taylor polynomial?
- Why would you ever want to find the Taylor series of a function?

Spring 2006, Math 104

**April and May, 2006**

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

(Last modified:
Monday, April 17, 2006,
12:10 PM )

I'll use Maple syntax for mathematical notation on this page.

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**

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

**Reading questions:**

**Reminders:**

__ Due Wednessday 4/5 at 9am__

**Section 11.2: Infinite Series, Convergence, and Divergence**

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

**Reading Questions: **

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

**Reminders:**

__ Due Friday 4/7 at 9am__

**Section 11.3: Testing for Convergence; Estimating Limits **

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

**Reading questions:**

__ Due Monday 4/10 at 9am__

**Section 11.3 Testing for Convergence; Estimating Limits**

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

**Reading Questions: **

**Reminders: **

__ Due Wednesday 4/12 at 9am__

**Re-read Section 11.3, through the Integral Test**

**No Reading Questions Today**

**Reminders: **

__ Due Friday 4/14 at 9am__

**Work on Project 2**

**No Reading Questions Today**

__ Due Monday 4/17 at 9am__

**Continue working on Project 2**

**No Reading Questions Today**

**Reminders:**

__ Due Wednesday 4/19 at 9am__

**Section 11.3 Testing for Convergence; Estimating Limits**

**No Reading Questions Today**

**Reminder:**

__ Due Friday 4/21 at 8am__

**Section 11.3 Testing for Convergence; Estimating Limits**

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

**Reading Questions:**

__ Due Monday 4/24 at 9 am__

**Section 11.4 Absolute Convergence; Alternating Series**

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

**Reading Questions: **

**Reminders:**

__ Due Wednesday 4/26 at 9am__

**Section 11.5 Power Series **

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

**Reading Questions:**

__ Due Friday 4/28 at 9am__

**Section 11.5 Power Series **

**No Reading Questions Today**

__ Due Monday 5/1 at 9am__

**Bring Questions for Exam 3 **

**No Reading Questions Today! **

**Reminders:**

__ Due Wednesday 5/3 at 9am__

**Section 11.5 Power Series **

**No Reading Questions Today**

__ Due Friday 5/5 at 9am__

**Section 11.6 Power Series as Functions **

**Section 11.7 Taylor Series**

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

**Reading Questions: **

Department of Mathematics and Computer Science

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TEL (508) 286-3973

FAX (508) 285-8278

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