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Math 104 - Calculus II - Reading Assignments
September 1999
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Be sure to check back, because this may change during the semester.
(Last modified:
Thursday, September 2, 1999,
2:41 PM )
I'll use Maple syntax for mathematical notation on this page.
All numbers indicate sections from Ostebee/Zorn, Vol 2.
For September 10
Course Policies
Notes on Reading Assignments
Section 5.1 Areas and Integrals
Section 5.2 The Area Function
Section 5.3 The Fundamental Theorem of Calculus
- To read : All, but you may skip the proof of the Fundamental Theorem of Calculus beginning on page 373.
The major ideas in these sections should be review for you.
- Be sure to understand :
The statement of both the first and second forms of the Fundamental Theorem; Example 3 in Section 5.3
Email Subject Line : Math 104 9/10 Your Name
Reading Questions :
- Does every continuous function have an antiderivative? Why or why not?
- If f(x)=3x-5 and a=2, where is Af increasing? decreasing? Why?
- Find the area between the x-axis and the graph of f(x)=x3 + 4 from x=0
to x=3.
For September 13
Section 5.4 Approximating Sums
- To read : All
- Be sure to understand :
The figures on page 378 and the section Sigma Notation; Partitions
begining on page 380
Email Subject Line : Math 104 9/13 Your Name
Reading Questions :
- When approximating an integral, which would you expect to be more accurate,
L10 or L100? Why?
- Give an example of a partition of the interval [0,3].
- What is a Riemann sum? Explain in your own words.
For September 15
Section 7.1 The Idea of Approximation
- To read :
All
- Be sure to understand :
The statement of Theorem 1
Email Subject Line : Math 104 9/15 Your Name
Reading Questions :
- Why would we ever want to approximate an integral?
- Give an example of a function that is monotone on the interval [0,2].
- Let f(x)=x2. Does Theorem 1 apply to the integral int( f(x), x= -1. . 2) ? Explain.
For September 17
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 9/17 Your Name
Reading Questions :
- Explain in words what K1 is in Theorem 2.
- Find a value for K1 for int( x2, x= -1. . 2).
- 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 20
Work on Group Project 1. No Reading Assignment.
For September 22
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 9/22 Your Name
Reading Questions :
- Explain in words what K2 is in Theorem 2.
- Find a value for K2 for int( x2, x= -1. . 2).
- 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 24
The Big Picture
- To read :
Reread Section 7.3
- Be sure to understand :
Example 3
Email Subject Line : Math 104 9/24 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 27
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 9/27 Your Name
Reading Questions :
- What is the domain of the function arccos(x)? Why?
- Why are we studying the inverse trig functions now?
- Find one antiderivative of 1 / (1+x2).
For September 29
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 9/29 Your Name
Reading Questions :
- Explain the difference between a definite integral and an indefinite integral.
- What are the three steps in the process of substitution?
- Substitution attempts to undo one of the techniques of differentiation.
Which one is it?
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