Spring 2003 Math 104

March, 2003

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 3/3 at 8am

Section 9.1 Taylor Polynomials

• To read: All, but you can skip the section Trigonometric polynomials: Another nice family.
• Be sure to understand: The statement of Theorem 1, Example 7, adn the definition of the Taylor polynomial.

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

Explain the basic idea of the Taylor polynomial for a function f(x) at x=x0 in your own words.

Reminder:

• Bring questions on PS 5.
• 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 3/5 at 8am

Section 9.2 Taylor's Theorem: Accuracy Guarantees for Taylor Polynomials

• To read: All, but you can skip the section Proving Taylor's theorem.
• Be sure to understand: The statement of Theorem 2 and Examples 2 and 3.

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

What is the point of Theorem 2? Explain in your own words.
Reminders:
• Begin PS 6.

Due Friday 3/7 at 8am

Antidifferentiation Exam

Reminders:

• The final draft of Project 1 is due today.

Due Monday 3/10 at 8am

More on Taylor Polynomials

Reminders:

• Bring questions on PS 6.
• 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 3/12 at 8am

Work on Project 2

Reminders:

• Begin PS 7.

Due Friday 3/14 at 8am

Section 10.1: Improper Integrals: Ideas and Definitions

• Be sure to understand: The section Convergence and divergence: Formal definitions and Examples 1 - 5.

E-mail Subject Line: Math 104 Your Name 3/14

1. What are the two ways in which an integral may be improper?
2. Explain why int( 1/x2, x=1..infty) is improper. Does the integral converge or diverge?
3. Explain why int( 1/x2, x=0..1) is improper. Does the integral converge or diverge?

Reminders:

• You do have a reading assignment due the Monday after break.

Due Monday 3/24 at 8am

Section 10.2: Detecting Convergence, Estimating Limits

• Be sure to understand: The statements of Theorems 1 and 2 and Example 4.

E-mail Subject Line: Math 104 Your Name 3/24

1. If 0 < f(x) < g(x) and int( g(x), x=1. . infty) converges, will int(f(x), x=1. .infty) converge or diverge? Why?
2. There are two types of errors that arise in Example 4 for approximating int( 1/(x5 +1), x=1..infty). What are the two types?

Reminder:

• Bring questions on PS 7.
• The deadline for receiving full credit on the antidifferentiation exam is Friday.

Due Wednesday 3/26 at 8am

Class Cancelled due to Moratorium on Classes as Usual, to allow you to spend one day focusing on the war and what's involved.

Instead of coming to class, go to some of the open classes. For extra credit, turn in one page describing one or more open class you went to that is not a regular class of yours.

Reminders:

• Begin PS 8.
• Project 2 proposals are still due Friday. These need only consist of the functions you plan to use, a graph of the outline of your figure, before it's revolved, and a very brief description of what your figure is going to be.

Due Friday 3/28 at 8am

Section 10.2: Detecting Convergence, Estimating Limits

• Be sure to understand: Example 5.

E-mail Subject Line: Math 104 Your Name 3/28

Suppose that 0 < f(x) < g(x).

1. If int(f(x), x=1. .infty) diverges, what can you conclude about int( g(x), x=1. . infty)?
2. If int(g(x), x=1. .infty) diverges, what can you conclude about int( f(x), x=1. . infty)?
3. If int(f(x), x=1. .infty) converges, what can you conclude about int( g(x), x=1. . infty)?

Reminders:

• Proposals for Project 2 due today.
• Exam 2 is next Tuesday. As decided in class Monday, you may take the exam Tuesday from 12:30-2 or at night. If you can't take it at night, but think you might need more than 1 1/2 hours on the exam, come talk to me so we can be sure to arrange a time.

Monday 3/31 at 8am

Questions for Exam 2

Reminder:

• PS 8 will not be turned in, but will be partially covered on this 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 decided in class Monday, you may take the exam Tuesday from 12:30-2 or at night. If you can't take it at night, but think you might need more than 1 1/2 hours on the exam, come talk to me so we can be sure to arrange a time.

Here ends the reading for March
Next, go to the reading for April and May!

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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