Reading Assignments for Calculus 2
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
- 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
Reading questions:
- 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?
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
- To read:
Finish the section and reread through Example 4.
- Be sure to understand:
The nth term test.
E-mail Subject Line: Math 104 Your Name 4/5
Reading Questions:
What does the nth Term Test tell you about each series? Explain.
- sum(sin(k), k=0..infinity)
- sum(1/k , k=1..infinity)
Reminders:
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
Reading questions:
- 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
Reading Questions:
- Explain in a couple sentences why the Integral Test makes sense.
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:
- 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
- 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.
No Reading Questions Today
Reminder:
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
Reading Questions:
- 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
- To read:
All
- Be sure to understand:
The statements of the Alternating Series test
E-mail Subject Line: Math 104 Your Name 4/24
Reading Questions:
- 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 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
- To read:
All
- Be sure to understand:
Examples 4 and 5.
E-mail Subject Line: Math 104 Your Name 4/26
Reading Questions:
- 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.
Reminders:
Due Friday 4/28 at 9am
Section 11.5 Power Series
- To read:
Re-read this section
- Be sure to understand:
The whole thing!
No Reading Questions Today
Due Monday 5/1 at 9am
Bring Questions for Exam 3
No Reading Questions Today!
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
- To read:
Re-read this section
- Be sure to understand:
The whole thing!
No Reading Questions Today
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
Reading Questions:
- 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?
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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