Reading Assignments for Calculus 2
    Fall 2009, Math 104

    November and December, 2009



    Be sure to check back often, because assignments may change!
    (Last modified: Wednesday, January 18, 2012, 12:36 PM )


    I'll often use Maple syntax for mathematical notation on this page.
    All section and page numbers refer to sections from Calculus: Early Transcendental Functions, Smith and Minton, 3rd Edition.



    Due Monday 11/2 at 9am

    Section 8.2: Infinite Series

    E-mail Subject Line: Math 104 Your Name 11/2

    Reading Questions:

    What does the kth Term Test tell you about each of the following series? Explain.

    1. sum(sin(k), k=0..infinity)
    2. sum(1/k , k=1..infinity)

    Reminders:


    Due Wednesday 11/4 at 9am

    Section 8.3: The Integral Test and Comparison Tests

    E-mail Subject Line: Math 104 Your Name 11/4

    Reading Questions:

    1. Explain in a couple of sentences (in your own words, of course) why the integral test makes sense. That is, explain the idea behind the integral test.

    Reminders:


    Due Friday 11/6 at 9am

    Section 8.3: The Integral Test and Comparison Tests

    E-mail Subject Line: Math 104 Your Name 11/6

    Reading questions:

    1. Explain in a couple of sentences why the Comparison Test makes sense. That is, explain the idea behind it.

    Reminders:


    Due Monday 11/9 at 9am

    Section 8.3: The Integral Test and Comparison Tests

    No Reading Question Today


    Due Wednesday 11/11 at 9am

    Section 8.3: The Integral Test and Comparison Tests

    E-mail Subject Line:Math 104 Your Name 11/11

    Reading questions:
    Consider the series sum( 12+3j, j=0..infinity). (This is Maple notation for a sum or series).

    1. Show that the series converges.
    2. Estimate the limit of the series within 0.01.
    3. Is your estimate an over- or under- estimate?

    Reminders:


    Due Friday 11/13 at 9am

    Continue Working on Project 1

    No Reading Questions Today

    Reminders:


    Due Monday 11/16 at 9am

    Section 8.3: The Integral Test and Comparison Tests

    E-mail Subject Line: Math 104 Your Name 11/16

    Consider the series sum( 1(k4+5), k=1..infinity). (This is Maple notation for a sum or series).

    1. Show that the series converges.
    2. Estimate the limit of the series within 0.01.
    3. Is your estimate an over- or under- estimate?

    Reminder:


    Due Wednesday 11/18 at 9am

    Section 8.4: Alternating Series

    E-mail Subject Line: Math 104 Your Name 11/18

    Reading Questions:

    1. Does sum( (-1)ksqrt(k), k=1..∞) converge or diverge?
    2. How closely does S100 approximate the series sum((-1)k (1/k), k=1 .. infinity) ? Why?

    Reminder:


    Due Friday 11/20 at 9am

    Section 8.5: Absolute Convergence and the Ratio Test

    E-mail Subject Line: Math 104 Your Name 11/20

    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.
    Reminders:


    Due Monday 11/23 at 9am

    Section 8.5: Absolute Convergence and the Ratio Test

    E-mail Subject Line: Math 104 Your Name 11/23

    Reading Questions:

    1. Explain in a couple of sentences why the Ratio Test makes sense.
    Reminders:


    Due Wednesday 11/25 at 9am

    Thanksgiving Break!


    Due Friday 11/27 at 9am

    Thanksgiving Break!


    Due Monday 11/30 at 9am

    Section 8.6: Power Series

    E-mail Subject Line: Math 104 Your Name 11/30

    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? Why have we not discussed the interval of convergence before? Explain in your own words.
    Reminders:


    Due Wednesday 12/2 at 9am

    Bring Questions for Exam 3

    No Reading Questions Today!
    Reminders:


    Due Friday 12/4 at 9am

    Section 8.6: Power Series

    E-mail Subject Line: Math 104 Your Name 12/4

    Reading Questions:

    1. Suppose the power series sum(bk(x-c)k, k=0..∞) has a non-trivial and non-infinite interval of convergence. Where will the midpoint of that interval be?
    Reminder:


    Due Monday 12/7 at 9am

    Section 8.6: Power Series

    E-mail Subject Line: Math 104 Your Name 12/7

    Reading Questions:

    1. As you have read, we can differentiate and integrate a convergent power series term-by-term. Why is this not obvious?
    2. Why might you want or need to use a power series?


    Due Wednesday 12/9 at 9am

    Section 8.7: Taylor Series

    E-mail Subject Line: Math 104 Your Name 12/9

    Reading Questions:

    1. How does a Taylor series differ from a Taylor polynomial?
    2. Give two good reasons for writing a known function ( such as cos(x) ) as a power series.

    Reminder:


    Due Friday 12/11 at 9am

    Section 8.8: Applications of Taylor Series

    E-mail Subject Line: Math 104 Your Name 12/11

    Reading Questions:

    1. If you wanted to find exp(sqrt(3)) using a Taylor series, what would you as a base point?
    Reminder:


    Here ends the reading for the Semester!


    Janice Sklensky
    Wheaton College
    Department of Mathematics and Computer Science
    Science Center, Room 101A
    Norton, Massachusetts 02766-0930
    TEL (508) 286-3973
    FAX (508) 285-8278
    jsklensk@wheatonma.edu


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