Math 104 - Calculus II - Reading Assignments - September 2001

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

For September 7

Section 5.1 Areas and Integrals
Section 5.2 The Area Function
Section 5.3 The Fundamental Theorem of Calculus
Section 5.4 Approximating Sums

To read : All, but you may skip the proof of the Fundamental Theorem of Calculus beginning on page 373. The major ideas in sections 5.1, 5.2, and 5.3 should be review for you.

Be sure to understand : The figures on page 378 and the section Sigma Notation; Partitions begining on page 380

Email Subject Line : Math 104 9/7 Your Name

Reading Questions :

1. When approximating an integral, which would you expect to be more accurate, L₁₀ or L₁₀₀? Why?
2. Give an example of a partition of the interval [0,3].
3. What is a Riemann sum? Explain in your own words.

For September 10

Section 7.1 The Idea of Approximation

To read : All

Be sure to understand : The statement of Theorem 1

Email Subject Line : Math 104 9/10 Your Name

Reading Questions :

1. Why would we ever want to approximate an integral?
2. Give an example of a function that is monotone on the interval [0,2].
3. Let f(x)=x². Does Theorem 1 apply to the integral int( f(x), x= -1. . 2) ? Explain.

For September 12

Section 7.2 More on Error: Left and Right Sums and the First Derivative

To read : All

Be sure to understand : The statement of Theorem 2

Email Subject Line : Math 104 9/12 Your Name

Reading Questions :

1. Explain in words what K₁ is in Theorem 2.
2. Find a value for K₁ for int( x², x= -1. . 2).
3. Use Theorem 2 and your value for K₁ to find an upper bound on the error when using L₁₀₀ to approximate int( x², x= -1. . 2).

For September 14

Section 7.3 Trapezoid Sums, Midpoint Sums, and the Second Derivative

To read : All

Be sure to understand : The statement of Theorem 3

Email Subject Line : Math 104 9/14 Your Name

Reading Questions :

1. Explain in words what K₂ is in Theorem 2.
2. Find a value for K₂ for int( x², x= -1. . 2).
3. Use Theorem 3 and your value for K₂ to find an upper bound on the error when using M₁₀₀ to approximate int( x², x= -1. . 2).

For September 17

The Big Picture on Chapter 7

To read : Reread Section 7.3

Be sure to understand : Example 3

Email Subject Line : Math 104 9/17 Your Name

Reading Question:

How many subdivisions does the trapezoid method require to approximate int( cos(x³), x = 0. . 1) with error less than 0.0001?

For September 19

For September 21

Section 3.8 Inverse Trigonometric Functions and Their Derivatives

To read : All, but you can skip the section on Inverse Trigonometric Functions and the Unit Circle

Be sure to understand :

Email Subject Line : Math 104 9/21 Your Name

Reading Questions :

1. What is the domain of the function arccos(x)? Why?
2. Why are we studying the inverse trig functions now?
3. Find one antiderivative of 1 / (1+x²).

For September 24

Section 6.1 Antiderivatives: The Idea
Section 6.2 Antidifferentiation by Substitution

To read : All

Be sure to understand : Examples 3, 5, and 8 from Section 6.2

Email Subject Line : Math 104 9/24 Your Name

Reading Questions :

1. Explain the difference between a definite integral and an indefinite integral.
2. What are the three steps in the process of substitution?
3. Substitution attempts to undo one of the techniques of differentiation. Which one is it?

For September 26

Q & A for Exam 1 today. No Reading Assignment.

For September 28

Section 9.1 Integration by Parts

To read : Through page 497. Be warned that Example 8 is a bit slippery.

Be sure to understand : The statement of Theorem 1 and Examples 1, 3, and 6

Email Subject Line : Math 104 9/28 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).