Reading Assignments for Calculus 2
Spring 2003, Math 104
April and May, 2003
Be sure to check back often, because assignments may change!
(Last modified:
Friday, April 18, 2003,
8:46 AM )
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 Wednesday 4/2 at 8am
Section 4.2 More on Limits: Limits Involving Infinity and l'Hopital's Rule
Section 11.1 Sequences and Their Limits
- To read:
The section l'Hopital's rule: finding limits by differentiation
that begins on page S-19 and all of Section 11.1.
- Be sure to understand:
The statement of l'Hopital's rule and the section Terminology and basic examples in Section 11.1.
E-mail Subject Line: Math 104 Your Name 4/2
Reading Questions:
- Does l'Hopital's Rule apply to lim_{(x -> infty)} x^{2} / e^{x} ?
Why or why not?
- Does l'Hopital's Rule apply to lim_{(x -> infty)} x^{2} / sin(x) ? Why or why not?
- Does the following sequence converge or diverge? Be sure to explain your answer.
1, 3, 5, 7, 9, 11, 13, . . .
- Find a symbolic expression for the general term a_{k} of the sequence
1, 2, 4, 8, 16, 32, . . .
Reminders:
- Begin PS 9.
- Return to working on the project.
Due Friday 4/4 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 sections Why series matter: A look ahead and Definitions and terminology.
E-mail Subject Line: Math 104 Your Name 4/4
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?
Due Monday 4/7 at 8am
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 4/7
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:
- Bring questions on PS 9.
- If you'd like to meet with Rachel Sunday night at 8pm in SC A118, please e-mail her by 5pm Sunday asking her to meet with you, and giving her a list of questions you have. Her e-mail address is rzeigowe.
Due Wednesday 4/9 at 8am
Section 11.3: Testing for Convergence; Estimating Limits
- To read:
The statements of the Comparison test and Integral test for non-negative series.
- Be sure to understand:
E-mail Subject Line: Math 104 Your Name 4/9
Reading questions:
- Explain in a couple of sentences why the Comparison Test makes sense.
- Explain in a couple sentences why the Integral Test makes sense.
Reminders:
- Begin PS 10.
- Project 2 is due Friday.
Due Friday 4/11 at 8am
Section 11.3 Testing for Convergence; Estimating Limits
- To read:
Finish the section
- Be sure to understand:
The ratio test
E-mail Subject Line: Math 104 Your Name 4/11
Reading Questions:
- Explain in a couple of sentences why the Ratio Test makes sense.
Due Monday 4/14 at 8am
Section 11.3 Testing for Convergence; Estimating Limits
- To read:
Really carefully re-read this section.
- Be sure to understand:
How it all fits together; when we can use each test.
No Reading Questions Today
Reminders:
- Bring questions on PS 10.
- If you'd like to meet with Rachel Sunday night at 8pm in SC A118, please e-mail her by 5pm Sunday asking her to meet with you, and giving her a list of questions you have. Her e-mail address is rzeigowe.
Due Wednesday 4/16 at 8am
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 4/16
Reading Questions:
- Give an example of a series that is conditionally convergent. Explain.
- Give an example of a series that is absolutely convergent. Explain.
Reminders:
- Begin PS 11.
- Exam 3 is next Tuesday.
Due Friday 4/18 at 8am
Section 11.4 Absolute Convergence; Alternating Series
- To read:
Re-read the section.
- Be sure to understand:
E-mail Subject Line: Math 104 Your Name 4/18
Reading Questions:
- How close does S_{100} approximate the series
sum((-1)^{k} (1/k), k=0 .. infinity) ?
Why?
Due Monday 4/21 at 8am
Bring Questions for Exam 3
No Reading Questions Today!
Reminder:
- PS 11 will not be collected, but it will be covered on the exam.
- If you'd like to meet with Rachel Sunday night at 8pm in SC A118, please e-mail her by 5pm Sunday asking her to meet with you, and giving her a list of questions you have. Her e-mail address is rzeigowe.
- As always, you may have handwritten notes on one side of a standard sheet of paper, and you may begin the exam at 12:30 on Tuesday.
Due Wednesday 4/23 at 8am
Section 11.5 Power Series
- To read:
All
- Be sure to understand:
Examples 4 and 5.
E-mail Subject Line: Math 104 Your Name 4/23
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.
Reminder:
Due Friday 4/25 at 8am
Section 11.5 Power Series
- To read:
Reread the section.
- Be sure to understand:
No Reading Questions Today
Due Monday 4/28 at 8am
Section 11.6 Power Series as Functions
- To read:
All
- Be sure to understand:
E-mail Subject Line: Math 104 Your Name 4/28
Reading Questions:
Give two good reasons for writing a known function ( such as cos(x) ) as a power series.
Reminders:
- Bring questions on PS 12.
- If you'd like to meet with Rachel Sunday night at 8pm in SC A118, please e-mail her by 5pm Sunday asking her to meet with you, and giving her a list of questions you have. Her e-mail address is rzeigowe.
Due Wednesday 4/30 at 8am
Section 11.7 Taylor Series
- To read:
All
- Be sure to understand:
The definition of a Taylor series.
E-mail Subject Line: Math 104 Your Name 4/30
Reading Questions:
- How does a Taylor series differ from a Taylor polynomial?
- Why would you ever want to find the Taylor series of a
function?
Reminder:
- The take-home portion of your final is due Tuesday May 6 at 2pm; the in class will be Tuesday from 2-5pm.
Due Friday 5/2 at 8am
Section 11.7 Taylor Series
- To read:
Re-read the section
- Be sure to understand:
No Reading Questions Today
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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