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Reading Assignments - Math 104 Calculus II - Fall 2010

Be sure to check back, because this may change during the semester.
(Last modified: Friday, November 26, 2010, 12:01 PM )

I'll use Maple syntax for mathematical notation on this page. All numbers indicate sections from Calculus, Early Transcendental Functions 3e by Smith and Minton.

For Friday September 3

4.1 Antiderivatives
4.2 Sums & Sigma Notation
4.3 Area
4.4 The Definite Integral

To read: This should all be review, so you can skim these sections. You can also skip the part in Section 4.2 on induction.

Be sure to understand: Example 2.3, Theorem 2.2, Example 3.2, Definition 3.2, Definition 4.1, and Example 4.2

Reading Questions:

  1. Give two different antiderivatives of f(x)=3x2 + cos(x).
  2. Explain the idea of a Riemann sum in your own words.
  3. Give an example of a partition of [0,4].

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For Wednesday September 8

Section 4.5 The Fundamental Theorem of Calculus
Section 2.8 Inverse Trigonometric Functions

To read: All of Section 4.6. Skip the first part of Section 2.8, but read the part on Inverse Trig Functions on pp 221-224.

Be sure to understand: Theorems 5.1 and 5.2, Example 5.3

Reading Questions:

  1. Find the area between the x-axis and the graph of f(x)=4/x + cos(x) between x=1 and x=2.
  2. Does every continuous function have an antiderivative? Why or why not?
  3. Why do you think we studying the inverse trig functions now?

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For Friday September 10

Section 4.6 Integration by Substitution

To read: All

Be sure to understand: Examples 6.3, 6.6, and 6.10

Reading Questions:

  1. Substitution attempts to undo one of the techniques of differentiation. Which one is it?
  2. Give one antiderivative of (3x2) / (1 + (x3)^2 )

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For Monday September 13

Section 4.7 Numerical Integration

To read: Up to the section on Simpson's Rule on page 407

Be sure to understand: Examples 7.1 and 7.5

Reading Questions:

  1. Why would we want to approximate an integral?
  2. When approximating an integral, which would you expect to be more accurate, M10 or M100? Why?
  3. If a function f(x) is concave down on an interval, will the trapezoidal rule over-estimate or under-estimate the integral? Why?

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For Wednesday September 15

Section 4.7 Numerical Integration

To read: The section on Error Bounds for Numerical Integration beginning on page 410

Be sure to understand: Theorem 7.1, Examples 7.10 and 7.11

Reading Questions:

  1. Explain in words what K represents in Theorem 7.1
  2. Consider the integral int( x3, x=-2..1). Is 4 a valid value for K in Theorem 7.1? Explain.

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For Friday September 17

Section 5.1 Area Between Curves
Section 5.2 Volume: Slicing, Disks, and Washers

To read: All of Section 5.1 and Section 5.2 through page 448

Be sure to understand: Examples 1.1, 1.4, 1.5, Remarks 2.1 and 2.2, Examples 2.1, 2.4 and 2.5

Reading Questions:

  1. Find the area bounded by the graphs y=x2 and y=-2x+3.
  2. Let R be the rectangle formed by the x-axis, the y-axis, and the lines y=1 and x=3. Describe the shape of the solid formed when R is rotated about the x-axis.
  3. Let T be the triangle formed by the lines y=2x, y=6 and the y-axis. Describe the shape of the solid formed when T is rotated about the y-axis.

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For Monday September 20

Section 5.2 Volume: Slicing, Disks, and Washers

To read: Finish the section

Be sure to understand: All

Reading Questions:

  1. Let T be the triangle formed by the lines y=2x, y=6 and the y-axis. Describe the shape of the solid formed when T is rotated about the x-axis.
  2. Let T be the same triangle as in #1. Describe the shape of the solid formed when T is rotated about the line y=8.

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For Wednesday September 22

Section 5.3 Volumes by Cylindrical Shells

To read: All

Be sure to understand: Examples 3.2 and 3.4

Reading Questions:

  1. Give an example where you would use cylindrical shells rather than washers to find volume.
  2. When using shells to find the volume of a solid formed by rotating about the y-axis, what is the variable of integration?
  3. When using washers to find the volume of a solid formed by rotating about the y-axis, what is the variable of integration?

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For Friday September 24

Reread Section 5.3, but no Reading Questions for today.

For September 27

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

For Wednesday September 29

Section 5.4 Arc Length and Surface Area

To read: All

Be sure to understand: Example 4.1 and 4.5

Reading Questions:

  1. Set up the integral that gives the length of the curve y=sin(2x) from x=0 to x=2*Pi.
  2. Set up the integral that gives the surface area of the surface formed when the curve y=x2 + 2 from x=0 to x=3 is rotated about the x-axis.

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For Friday October 1

Work on Project 1 in class. No Reading Questions for today.

For Monday October 4

Work on Project 1 in class. No Reading Questions for today.

For Wednesday October 6

Section 6.2 Integration by Parts

To read: All

Be sure to understand: Examples 2.2, 2.4, and 2.5

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 * ex, x).
    Use parts to find an antiderivative for x * ex.

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For Friday October 8

Reread Section 6.2, but no Reading Questions for today.

For Wednesday October 13

Review techniques of antidifferentiation. No Reading Questions for today.

For Friday October 15

Antidifferentiation Exam. No Reading Questions for today.

For Monday October 18

Section 6.6 Improper Integrals

To read: Through page 555, up to the section on the Comparision Test

Be sure to understand: Definitions 6.1 and 6.3, Examples 6.2, 6.3, 6.6, and 6.7

Reading Questions:

  1. Explain why int( 1/x2, x=1..infty) is improper.
  2. Explain why int( 1/x2, x=0..5) is improper.
  3. Explain why int( 1/x2, x=-5..5) is improper.

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For Wednesday October 20

Section 6.6 Improper Integrals

To read: Finish the section, beginning on page 555 with the section on the Comparision Test

Be sure to understand: Theorem 6.1, Examples 6.14 and 6.16, and the box Beyond Formulas on page 558

Reading Questions: Suppose that 0 < f(x) < g(x).

  1. If int(f(x), x=1. .infty) diverges, what can you conclude about int( g(x), x=1. . infty)?
  2. If int(g(x), x=1. .infty) diverges, what can you conclude about int( f(x), x=1. . infty)?
  3. If int(f(x), x=1. .infty) converges, what can you conclude about int( g(x), x=1. . infty)?

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For Friday October 22

Reread Section 6.6, but no Reading Questions for today.

For Monday October 25

Section 3.2 l'Hopital's Rule
Section 8.1 Sequences of Real Numbers

To read: All of Section 3.2; through the statement of Theorem 1.4 on page 621 in Section 8.1

Be sure to understand: Examples 2.3, 2.4 in Section 3.2; Examples 1.5, 1.9 in Section 8.1

Reading Questions:

  1. Does l'Hopital's Rule apply to lim(x -> infty) x2 / ex ? Why or why not?
  2. Does l'Hopital's Rule apply to lim(x -> infty) x2 / sin(x) ? Why or why not?
  3. Does the following sequence converge or diverge? Be sure to explain your answer.
    1, 3, 5, 7, 9, 11, 13, . . .
  4. Find a symbolic expression for the general term ak of the sequence
    1, 2, 4, 8, 16, 32, . . .

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For Wednesday October 27

Section 8.2 Infinite Series

To read: All

Be sure to understand: Examples 2.1 and 2.4; Theorem 2.1

Reading Questions:

  1. There are two sequences associated with every series. What are they?
  2. Does the geometric series Σ (1/4)k converge or diverge? Why?

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For Friday October 29

Section 8.2 Infinite Series

To read: Reread the Section

Be sure to understand: The kth Term Test

Reading Questions: What does the kth Term Test tell you about each series? Explain.

  1. Σ 2k
  2. Σ 1/k

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For Monday November 1

Q & A for Exam 2. No Reading Questions for today.

For Wednesday November 3

Section 8.3 The Integral Test and Comparison Tests

To read: Through page 640

Be sure to understand: Examples 3.1 and 3.3

Reading Question:

    Explain in a couple of sentences why you think the Integral Test should hold.

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For Friday November 5

Section 8.3 The Integral Test and Comparison Tests

To read: The section on the Comparison Test, pp 642 - 644

Be sure to understand: Examples 3.5, 3.6, and 3.7

Reading Questions:

    Explain in a couple of sentences why you think the Comparison Test should hold.

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For Monday November 8

Section 8.4 Alternating Series

To read: All

Be sure to understand: Examples 4.1, 4.2, 4.5 and 4.6

Reading Questions: Consider the series Σ (-1)^(k+1) /k^2

  1. Why does this series converge?
  2. How closely does S50 approximate the value of the series? Why?

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For Wednesday November 10

Work on Project 2 in class. No Reading Questions for today.

For Friday November 12

Section 8.5 Absolute Convergence and the Ratio Test

To read: All, but you can skip the section on the Root Test

Be sure to understand: Examples 5.3 and 5.5

Reading Questions:

  1. Give an example of a series that is conditionally convergent. Explain.
  2. Give an example of a series that is absolutely convergent. Explain.

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For Monday November 15

Reread Section 8.5, but no Reading Questions for today.

For Wednesday November 17

Section 8.6 Power Series

To read: All

Be sure to understand:

Reading Questions:

  1. How do power series differ from the series we have looked at up to this point?
  2. What is the interval of convergence of a power series? Explain in your own words.

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For Friday November 19

Reread Section 8.6, but no Reading Questions for today.

For Monday November 22

Section 8.7 Taylor Series

To read: All. This can be tough going, but we'll discuss the section thoroughly in class.

Be sure to understand: Examples 7.1, 7.4 and 7.5

Reading Question:

    What is the basic idea of constructing a Taylor series for a function f(x)? Explain in your own words.

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For Monday November 29

Q & A for Exam 3. No Reading Questions for today.

For Wednesday December 1

Tying up some loose ends on infinite series. No Reading Assignment for today.

For Friday December 3

Section 9.4 Polar Coordinates

To read: All

Be sure to understand: Examples 4.2, 4.7, and 4.10

Reading Questions:

  1. Why would we ever use polar coordinates rather than rectangular coordinates?
  2. Give two different representations in polar coordinates for the point with rectangular coordinates (sqrt(3), 1).
  3. What is the relationship between the graphs y=sin(x) and y=sin(2x) in rectangular coordinates?
  4. What is the relationship between the graphs r=sin(θ) and r=sin(2θ) in polar coordinates?

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For Monday December 6

Section 9.5 Calculus and Polar Coordinates

To read: From the middle of page 757 through Example 5.7. We'll focus on integration in polar coordinates this week and pick up the part on differentiation next semester in Multivariable Calculus.

Be sure to understand: Examples 5.3, 5.4 and 5.5

Reading Questions:

Consider the polar "rectangle" R described by α ≤ θ ≤ β and 0 ≤ r ≤ R.

  1. What is the shape of R?
  2. What is the area of R?

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For Wednesday December 8

Reread Section 9.5, but no Reading Questions for today.

For Friday December 10

The BIG Picture for the course

No reading for today
Last Modified: Friday, November 26, 2010, 12:01 PM
Maintained by: ratliff_thomas@wheatoncollege.edu