Math 102  Calculus I with Economics Applications
Reading Assignments  November & December 2003
Be sure to check back, because this may change during the semester.
(Last modified:
Sunday, August 17, 2003,
2:11 PM )
I'll use Maple syntax for mathematical notation on this page.
All numbers indicate sections from Calculus from Graphical, Numerical, and Symbolic Points of View, Second Edition by Ostebee/Zorn.
For Monday November 3
Section 4.7 Building Polynomials to Order: Taylor Polynomials
To read : All. Be sure to understand Examples 5 and 8.
Reading Questions :
 Why would you want to find the Taylor polynomial of a function?
 In your own words, briefly explain the idea of building the Taylor polynomial
for a function f(x).
For Wednesday November 5
The Big Picture before Exam 2. No Reading Assignment.
For Friday November 7
Section 4.7 Building Polynomials to Order: Taylor Polynomials
Reread the section, but no Reading Questions for today.
For Monday November 10
Section 4.8 Why Continuity Matters
To read : All. Be sure to understand the statement of the Intermediate
Value Theorem.
Reading Questions :
 What are the hypotheses of the Intermediate Value Theorem?
 What is the conclusion of the Intermediate Value Theorem?
For Wednesday November 12
Section 4.9 Why Differentiability Matters: The Mean Value Theorem
To read : All. Be sure to understand the statement of the Mean Value Theorem
and the section "What the MVT says".
Reading Questions :
 What are the hypotheses of the Mean Value Theorem?
 What is the conclusion of the Mean Value Theorem?
 Explain the MVT using "car talk" (that is, using velocity).
For Friday November 14
Section 5.1 Areas and Integrals
To read : All. Be sure to understand the definition of the integral, Example 2,
and the section "Properties of the integral" beginning on page 306.
Reading Questions :
 What does the integral of a function f from x=a to x=b measure?
 Is the integral of f(x)=5x from x=1 to x=3 positive or negative? Why?
For Monday November 17
Section 5.2 The Area Function
To read : All. Be sure to understand the definition of the area function
and Examples 2, 3, and 4.
Reading Questions :
 Let f be any function. What does the area function A_{f}(x) measure?
 Let f(t)=t and let a=0. What is A_{f}(1)?
For Wednesday November 19
Section 5.3 The Fundamental Theorem of Calculus
To read : All, but you can skip the proof of the FTC in the section. We'll look
at a different approach in class.
Reading Questions :
 Find the area between the xaxis and the graph of f(x)=x^{3} + 4 from x=0
to x=3.
 Does every continuous function have an antiderivative? Why or why not?
For Friday November 21
Section 5.3 The Fundamental Theorem of Calculus
To read : Reread the section for today.
Reading Questions :
 If f(x)=3x5 and a=2, where is A_{f} increasing? decreasing? Why?
 How would your answer change if a=0?
For Monday November 24
Section 5.4 Finding Antiderivatives: The Method of Substitution
To read : All. Be sure to understand Examples 8, 9, and 10.
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?
For Wednesday November 26 &
Friday November 28
Thanksgiving Break.
For Monday December 1
Section 5.4 Finding Antiderivatives: The Method of Substitution
Reread the section, but no Reading Questions for today.
For Wednesday December 3
The Big Picture before Exam 3. No Reading Assignment.
For Friday December 5
Section 5.6 Approximating Sums: The Integral as a Limit
To read : All. Be sure to understand the definition of a Riemann sum
and Example 3.
Reading Questions :
 Explain, in your own words, the idea of Riemann sums for approximating integrals.
 If f(x) is decreasing on [a,b], will L_{n} underestimate or overestimate
the integral of f from a to b? How about R_{n}?
For Monday December 8
Section Approximating Sums: The Integral as a Limit
Reread the section, but no Reading Questions for today.
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