Reading Assignments for Calculus 2
    Spring 2012, Math 104

    April and May, 2012



    Be sure to check back often, because assignments may change!
    (Last modified: Friday, April 27, 2012, 9:12 AM )


    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 4/2 at 8:30am

    Section 8.3: The Integral Test and Comparison Tests

    No Reading Questions Today

    Reminders:


    Due Wednesday 4/4 at 8:30am

    Project 2

    No Reading Questions Today

    Reminders:


    Due Friday 4/6 at 8:30am

    Section 8.3: The Integral Test and Comparison Tests

    Reading questions:

    1. Explain in a couple of sentences why the Comparison Test makes sense. That is, explain the idea behind it.
    2. Show that the series 1(2+3j) converges.

    Submit answers through OnCourse

    Reminders:


    Due Monday 4/9 at 8:30am

    Guide to Writing Mathematics
    Checklist
    Section 8.3: The Integral Test and Comparison Tests

    Consider the series 1(k4+5).

    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?

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    Reminders:


    Due Wednesday 4/11 at 8:30am

    Section 8.4: Alternating Series

    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 .. ∞) ? Why?

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    Reminders:


    Due Friday 4/13 at 8:30am

    Section 8.5: Absolute Convergence and the Ratio Test

    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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    Reminders:


    Due Monday 4/16 at 8:30am

    Section 8.5: Absolute Convergence and the Ratio Test

    Reading Questions:

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

    Submit answers through OnCourse


    Due Wednesday 4/18 at 8:30am

    Section 8.6: Power Series

    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.
    3. Suppose the power series bk(x-c)k has a non-trivial and non-infinite interval of convergence. Where will the midpoint of that interval be?
    4. As you have read, we can differentiate and integrate a convergent power series term-by-term. Why is this not obvious?
    5. Why might you want or need to use a power series?

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    Reminder:


    Due Friday 4/20 at 8:30am

    Section 8.7: Taylor Series

    Reading Questions:

    1. Give two good reasons for writing a known function ( such as cos(x) ) as a power series.

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    Reminders:

    Reminders:


    Due Monday 4/23 at 8:30am

    Section 8.7: Taylor Series

    No Reading Questions Today


    Due Wednesday 4/25 at 8:30am

    Questions for Exam 3

    Wheaton's Honor Code
    Wheaton's Description of Plagiarism
    Course policies

    To read: And again, re-read the Honor Code, Wheaton's description of plagiarism, and the portion in the course policies that applies to the Honor Code, paying particular attention to how it all applies to exam situations.

    No Reading Questions Today!
    Reminders:


    Due Friday 4/27 at 8:30am

    Section 8.8: Applications of Taylor Series

    Reading Questions:

    1. If you wanted to find esqrt(3) using a Taylor series, what would you use as a base point?

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    Reminder:


    Due Monday 4/30 at 8:30am

    Section 9.4: Polar Coordinates

    Reading Questions:

    1. Why might we use polar coordinates rather than rectangular coordinates?
    2. Give two different representations in polar coordinates of the point with rectangular coordinates (2sqrt(2), 2sqrt(2))
    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?

    Submit answers through OnCourse


    Due Wednesday 5/2 at 8:30am

    Section 9.5: Calculus and Polar Coordinates

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

    1. What is the shape of this "rectangle"?
    2. What is the area of this "rectangle"?

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    Reminder:


    Due Friday 5/4 at 8:30am

    The Big Picture

    No Reading Questions Today

    Reminder:


    Here ends the reading for the Semester!


    Janice Sklensky
    Wheaton College
    Department of Mathematics and Computer Science
    Science Center, Room 1306
    Norton, Massachusetts 02766-0930
    TEL (508) 286-3973
    FAX (508) 285-8278
    jsklensk@wheatonma.edu


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