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Reading Assignments - Math 104 Calculus II - Spring 2010

Be sure to check back, because this may change during the semester.
(Last modified: Wednesday, April 21, 2010, 10:17 AM )

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 January 29

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 Monday February 1

Section 4.5 The Fundamental Theorem of Calculus

To read: All

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?

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For Wednesday February 3

Section 2.8 Inverse Trigonometric Functions
Section 4.6 Integration by Substitution

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

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

Reading Questions:

  1. Why do you think we studying the inverse trig functions now?
  2. Substitution attempts to undo one of the techniques of differentiation. Which one is it?
  3. Give one antiderivative of (3x2) / (1 + (x3)^2 )

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For Friday February 5

Reread Section 4.6, but no Reading Questions for today.

For Monday February 8

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 integral, will the trapezoidal rule over-estimate or under-estimate the integral? Why?

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For Wednesday February 10

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 February 12

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 February 15

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 February 17

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

For Friday February 19

Section 5.3 Volumes by Cylindrical Shells

To read: All

Be sure to understand: Examples 3.2 and 3.4

Reading Questions:

  1. Why would you find a volume using cylindrical shells rather than using washers?
  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 Monday February 22

Reread Section 5.3, but no Reading Questions for today.

For Wednesday February 24

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 February 26

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

For Monday March 1

Section 6.1 Review of Formulas and Techniques

To read: All

Be sure to understand: Go through all Examples 1.1-1.5 in detail

Reading Questions:
None for today.

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For Wednesday March 3

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 March 5

Reread Section 6.2, but no Reading Questions for today.

For Monday March 8

Antidifferentiation Exam. No Reading Questions for today.

For Wednesday March 10

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 Friday March 12

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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March 15 - 19

Spring Break!

For Monday March 22

Reread Section 6.6, but no Reading Questions for today.

For Wednesday March 24

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 Friday March 26

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 Sigma (1/4)k converge or diverge? Why?

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For Monday March 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. Sigma 2k
  2. Sigma 1/k

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For Wednesday March 31

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

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For Friday April 2

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 Monday April 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 Wednesday April 7

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

For Friday April 9

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 (-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 Monday April 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 Wednesday April 14

Reread Section 8.5, but no Reading Questions for today.

For Friday April 16

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 Monday April 19

Reread Section 8.6, but no Reading Questions for today.

For Wednesday April 21

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 Friday April 23

Section 8.8 Applications of Taylor Series

To read: Through Example 8.5 on page 689.

Be sure to understand: Examples 8.1 and 8.4

Reading Question:

    Give two good reasons for finding the Taylor series for a known function, such as sin(x).

No reason to send this in. We've talked about this in class on Wednesday & Thursday. - TR

For Monday April 26

Section 12.1 Functions of Several Variables

To read: All

Be sure to understand: Examples 1.6 and 1.8

Reading Questions:

  1. For a function f(x,y), in what dimension does its graph z=f(x,y) lie?
  2. If f(x,y)=4x2 + 4y2, what is the shape of the level curve at f(x,y)=16?

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For Wednesday April 28

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

For Friday April 30

Section 12.3 Partial Derivatives

To read: All

Be sure to understand: Examples 3.1 and 3.2

Reading Questions: Let f(x,y)=x2y + 3xy - y.

  1. Find fx(x,y) and fy(x,y)
  2. Is f increasing or decreasing in the x direction at the point (2,1)? Why?

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For Monday May 3

Reread Section 12.3, but no reading for today.

For Wednesday May 5

Multivariable Optimization

No reading for today.

For Friday May 7

The BIG Picture for the course

No reading for today
Last Modified: Wednesday, April 21, 2010, 10:17 AM
Maintained by: ratliff_thomas@wheatoncollege.edu