Math 104 - Calculus II Reading Assignments - October 2002

Be sure to check back, because this may change during the semester.
(Last modified: Thursday, October 24, 2002, 3:19 PM )

I'll use Maple syntax for mathematical notation on this page.
All numbers indicate sections from Ostebee/Zorn, Vol 2, 2nd Edition.

For October 2

The Big Picture before Exam 1. No Reading Assignment for today.

For October 4

Section 7.3 Work

To read : All

Be sure to understand : The section Work as an integral and Examples 2 and 3.

Email Subject Line : Math 104 10/4 Your Name

Reading Questions :

1. What simplifying assumptions are made in this section? Are these completely realistic?
2. Why do we need to use calculus to calculate work when the force varies?

For October 7

Section 8.1 Integration by Parts

To read : All

Be sure to understand : Theorem 1. Be warned that Examples 8 and 9 can be a little slippery.

Email Subject Line : Math 104 10/7 Your Name

Reading Questions :

1. Integration by parts attempts to undo one of the techniques of differentiation. Which one is it?
2. Pick values for u and dv in the integral int( x * sin(x), x). Use parts to find an antiderivative for x * sin(x).

For October 9

Section 8.1 Integration by Parts

To read : Reread the section for today

Email Subject Line : Math 104 10/9 Your Name

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.

1. int( x*cos(x), x)
2. int(x*cos(x²),x)

For October 11

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, and the definition of the Taylor polynomial.

Email Subject Line : Math 104 10/11 Your Name

Reading Question :

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

For October 14

Fall Break. No Reading Assignment.

For October 16

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.

Email Subject Line : Math 104 10/16 Your Name

Reading Questions :

What is the point of Theorem 2? Explain in your own words.

For October 18

For October 21

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.

Email Subject Line : Math 104 10/21 Your Name

Reading Questions :

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

For October 23

For October 25

For October 28

Section 10.2 Detecting Convergence, Estimating Limits

To read : All

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

Email Subject Line : Math 104 10/28 Your Name

Reading Questions :

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?

For October 30

Section 10.2 Detecting Convergence, Estimating Limits

To read : Reread the section for today.

Be sure to understand : Example 5.

Email Subject Line : Math 104 10/30 Your Name

Reading Questions : 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)?