Reading Assignments for Calculus 2
Fall 2005 Math 104
October, 2005
Be sure to check back often, because assignments may change!
(Last modified:
Monday, August 29, 2005,
11:40 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 Monday 10/3 at 9am
Section 8.1 Integration by Parts(continued)
- To read:
All
- Be sure to understand:
Theorem 1. Be warned that Examples 8 and 9 can be a little slippery.
E-mail Subject Line: Math 104 Your Name 10/3
Reading questions:
- Integration by parts attempts to undo one of the techniques of differentiation. Which one is it?
- Pick values for u and dv in the integral int( x * sin(x), x). Use parts to find an antiderivative for x * sin(x).
Due Wednesday 10/5 at 9am
Section 8.1 Integration by Parts
Section 9.1 Taylor Polynomials
- To read: re-read Section 8.1 for Wednesday. For Thursday, read Section 9.1 (you may skip the section Trigonometric polynomials: Another nice family).
E-mail Subject Line: Math 104 Your Name 10/5
Reading questions:
Each integral can be evaluated using u-substitution or integration by parts. Which technique would you use in each case? You do not need
to evaluate the integral, but explain your choice.
- int( x*cos(x), x)
- int(x*cos(x^{2}),x)
Reminders:
- Continue taking advantage of the tutoring hours and my office hours, if you've been before; if you've never been, consider trying it for the first time.
- Bring unresolved problems on PS 5 to class.
- The math for project 1 should be finished by Wednesday evening at the latest.
Due Friday 10/7 at 9am
Section 9.1 Taylor Polynomials
- To read:
Re-read this section, combining what we discussed Thursday with the book's discussion to resolve as many of your previous difficulties as possible.
- Be sure to understand:
The statement of Theorem 1, Example 7, and the definition of the Taylor polynomial.
E-mail Subject Line: Math 104 Your Name 10/7
Reading questions:
Explain the basic idea of the Taylor polynomial for a function f(x)
at x=x_{0} in your own words.
Reminder:
- Begin PS 6.
- Use the
Guide to Writing Mathematics and the checklist to help you write your project.
- I urge you to bring me a draft of your project for some suggestions.
Due Monday 10/10 at 9am
Fall Break!
Due Wednesday 10/12 at 9am
Section 9.1 Taylor Polynomials
- To read:
Re-read this section yet again, trying to fit everything together.
No Reading Questions Today
Reminder:
- Come to my office hours, tutoring hours!
- Bring questions on PS 6.
- Everyone in your group should be proof-reading your project and making constructive comments. Remember that a blank copy of the check-list should be attached to your project when you turn it in.
Due Friday 10/14 at 9am
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 10/14
Reading Questions:
What is the point of Theorem 2? Explain in your own words.
Reminders:
- I'll give you the antidifferentiation exam toward the end of class.
- Begin PS 7.
Due Monday 10/17 at 9am
Section 9.2 Taylor's Theorem: Accuracy Guarantees for Taylor Polynomials
- To read:
Re-read this section.
E-mail Subject Line: Math 104 Your Name 10/17
Reading Questions:
Let f(x)=sqrt(x).
- Find P_{3}(x) for f at the base point x_{0}=64.
- What can you say about the error committed by using
P_{3}(x) as an approx for sqrt(x) on the interval [50,80]?
Reminders:
- Mid-semester reminder -- office hours really are an important part of this course. If you haven't come in for questions yet, make a point of stopping in this week, whether it's to address a problem you wish you'd dealt with weeks ago, something that's confusing you know, a subtle point you'd like resolved, or to discuss how what we're learning connects to something you've learned in another class.
Due Wednesday 10/19 at 9am
Section 10.1: Improper Integrals: Ideas and Definitions
- To read:
All
- Be sure to understand:
The section Convergence and divergence: Formal definitions
and Examples 1 - 5.
E-mail Subject Line: Math 104 Your Name 10/19
Reading questions:
- What are the two ways in which an integral may be improper?
- Explain why int( 1/x^{2}, x=1..infinity) is improper. Does the integral converge or diverge?
- Explain why int( 1/x^{2}, x=0..1) is improper. Does the integral converge or diverge?
Reminders:
- Exam 2 is Thursday 10/27
- Bring questions on PS 7 to class.
Due Friday 10/21 at 9am
Section 10.2: Detecting Convergence, Estimating Limits
- To read:
All
- Be sure to understand:
The statements of Theorems 1 and 2 and Example 4.
E-mail Subject Line: Math 104 Your Name 10/21
Reading questions:
- 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?
- There are two types of errors that arise in Example 4 for approximating int( 1/(x^{5} +1), x=1..infty). What are the two types?
Reminders:
Due Monday 10/24 at 9am
Section 10.2: Detecting Convergence, Estimating Limits
- To read:
Reread the section.
- Be sure to understand:
Example 5.
E-mail Subject Line: Math 104 Your Name 10/24
Reading Questions:
Suppose that 0 < f(x) < g(x).
- If int(f(x), x=1. .infty) diverges, what can you conclude about int( g(x), x=1. . infty)?
- If int(g(x), x=1. .infty) diverges, what can you conclude about int( f(x), x=1. . infty)?
- If int(f(x), x=1. .infty) converges, what can you conclude about int( g(x), x=1. . infty)?
Reminders:
- Monday is the deadline for receiving full credit on the antidifferentiation exam. You really need antidifferentiation to come easily to you for the exam Thursday!
Wednesday 10/26 at 9am
Questions for Exam 2
No Reading Questions today
Reminder:
- Don't wait to bring all your questions your class on Wednesday -- we might not have time to get through them all. Bring some to my office hours and/or the tutoring hours.
- PS 8 will not be turned in, but will be covered on this exam.
- As before, you may have an 8 1/2 x 11 handwritten front-only sheet of notes, and you may begin the exam at 12:30.
Due Friday 10/28 at 9am
Section 10.2: Detecting Convergence, Estimating Limits
- To read:
Reread the section again.
No Reading Questions Today
Reminders:
Due Monday 10/31 at 9am
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 10/31
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, . . .
Here ends the reading for October
Next, go to the reading for November!
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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