
Math 104  Calculus II  Reading Assignments
February 1999

Be sure to check back, because this may change during the semester.
(Last modified:
Wednesday, January 20, 1999,
11:29 PM )
I'll use Maple syntax for mathematical notation on this page.
All numbers indicate sections from Ostebee/Zorn, Vol 2.
For February 3
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
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 these sections 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 2/3 Your Name
Reading Questions :
 When approximating an integral, which would you expect to be more accurate,
L_{10} or L_{100}? Why?
 Give an example of a partition of the interval [0,3].
 What is a Riemann sum?
For February 5
Section 7.1 The Idea of Approximation
 To read :
All
 Be sure to understand :
The statement of Theorem 1
Email Subject Line : Math 104 2/5 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)=x^{2}. Does Theorem 1 apply to the integral int( f(x), x= 1. . 2) ? Explain.
For February 8
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 2/8 Your Name
Reading Questions :
 Explain in words what K_{1} is in Theorem 2.
 Find a value for K_{1} for int( x^{2}, x= 1. . 2).
 Use Theorem 2 and your value for K_{1} to find an upper bound on the error when using L_{100} to approximate int( x^{2}, x= 1. . 2).
For February 10
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 2/10 Your Name
Reading Questions :
 Explain in words what K_{2} is in Theorem 2.
 Find a value for K_{2} for int( x^{2}, x= 1. . 2).
 Use Theorem 3 and your value for K_{2} to find an upper bound on the error when using M_{100} to approximate int( x^{2}, x= 1. . 2).
For February 12
The Big Picture
 To read :
Reread Section 7.3
 Be sure to understand :
Example 3
Email Subject Line : Math 104 2/12 Your Name
Reading Question:
How many subdivisions does the trapezoid method require to approximate
int( cos(x^{3}), x = 0. . 1) with error less than 0.0001?
For February 15
Work on Group Project 1. No Reading Assignment.
For February 17
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 2/17 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+x^{2}).
For February 19
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 2/19 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?
For February 22
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 2/22 Your Name
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).
For February 24
Section 9.1 Integration by Parts
 To read :
Reread the section
 Be sure to understand :
Example 8
Email Subject Line : Math 104 2/24 Your Name
Reading Questions :
Each integral can be evaluated using usubstitution or integration by parts. Which technique would you use in each case? Why?
 int( x*cos(x), x)
 int(x*cos(x^{2}),x)
For February 26
Exam 1 today. No Reading Assignment.
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