Reading Assignments - Math 104 - Calculus II
    January & February 1998

    I'll use Maple syntax for mathematical notation on this page.
    Be sure to check back often, because the assignments may change.

    For January 28

    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.
    • Be sure to understand: The major ideas in these sections should be review for you. If you aren't familar with the Area Function, don't despair: we'll talk about it in class.

    Email Subject Line: Math 104 1/28 Your Name

    Reading Questions:

    1. What does the integral of a function f from x=a to x=b measure?
    2. Let f(t)=t and let a=0. What is Af(2)?
    3. Find the area between the x-axis and the graph of y=x2 + 2 from x=0 to x=2.

    For January 30

    Section 5.4 Approximating Sums
    • To read: All. The integral defined as a limit can be tough to get a handle on.
    • Be sure to understand: The figures on page 378 and the section Sigma Notation; Partitions

    Email Subject Line: Math 104 1/30 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?

    For February 2

    Section 7.1 The Idea of Approximation
    • To read: All
    • Be sure to understand: The statement of Theorem 1

    Email Subject Line: Math 104 2/2 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 February 4

    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 2/4 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 February 6

    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 2/6 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 February 9

    The Big Picture
    • To read: Reread Section 7.3
    • Be sure to understand: Example 3

    Email Subject Line: Math 104 2/9 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 February 11

    Section 3.8 Inverse Trigonometric Functions and Their Derivatives
    This section is from Volume 1, but it is included in Volume 2 starting on page 733.
    • To read: All, but you can skip the section on Inverse Trigonometric Functions and the Unit Circle

    Email Subject Line: Math 104 2/11 Your Name

    Reading Questions:

    1. What is the domain of the function arccos(x)? Why?
    2. What is the range of arctan(x)?
    3. Find one antiderivative of 1 / (1+x2).

    For February 13

    No Reading Assignment today because of the project.

    For February 16

    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 2/16 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 February 18

    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 2/18 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 February 20

    No reading questions for today, but reread Section 9.1 Integration by Parts from Wednesday.

    For February 23

    Exam 1 today. No Reading Assignment.

    For February 25

    Section 8.1 Introduction to Using the Definite Integral
    Section 8.2 Finding Volumes by Integration
    • To read: All
    • Be sure to understand: The section from 8.2 on Reassembling Riemann's Loaf and Example 1 from 8.2.

    Email Subject Line: Math 104 2/25 Your Name

    Reading Questions:

    1. Let R be the rectangle formed by the x-axis, the y-axis, and the lines y=1 and x=3. What is the shape of the solid formed when R is rotated about the x-axis?
    2. Let T be the triangle formed by the lines y=x, x=1 and the x-axis. What is the shape of the solid formed when T is rotated about the x-axis?

    For February 27

    Antidifferentiation Exam today. No Reading Assignment.

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