Reading Assignments for Multivariable Calculus
    Spring 2007, Math 236

    April and May, 2007



    Be sure to check back often, because assignments may change!
    (Last modified: Thursday, April 12, 2007, 7:26 PM )


    I'll use Maple syntax for mathematical notation on this page.
    All section and page numbers refer to sections from Smith & Minton's Multivariable Calculus, 3rd edition.


    Due Monday 4/2 at 9am

    Section 13.1: Double Integrals

    E-mail Subject Line: Math 236 Your Name 4/2

    Reading questions:

    1. If f(x,y) is a positive function of two variables, what does _R f(x,y)dA measure?
    2. Explain Fubini's Theorem in your own words. What is its importance?

    Reminder:


    Due Wednesday 4/4 at 9am

    Section 13.1: Double Integrals (continued)

    E-mail Subject Line: Math 236 Your Name 4/4

    Reading questions:
    In the double integral R f(x,y)dA,

    1. What does dA represent?
    2. Do the two integral signs go together -- that is, are they, in a sense, a new symbol? Or do they represent first one integral and then another?


    Due Friday 4/6 at 9am

    13.2: Area, Volume, and Center of Mass

    E-mail Subject Line: Math 236 Your Name 4/6

    Reading questions:

    1. If R is the circle of radius 3 centered at the point (5,1), what is R dA? (You should be able to do this without setting up any iterated integral)
    2. Is My used to compute the x- or the y- coordinate of the center of mass? And in a related question -- why do you think it's called My?
    Reminders:


    Due Monday 4/9 at 9am

    Section 9.4: Polar Coordinates, Section 13.3: Double Integrals in Polar Coordinates

    E-mail Subject Line: Math 236 Your Name 4/9

    Reading questions:

    1. Find one polar coordinate representation for the rectangular point (5,-2).
    2. Find rectangular coordinates for the polar point (1,Pi/3).
    3. The graphs of (a) r=sin(7*theta) and of (b) r=sin(7*theta)+5 are shown below. Match the functions to the graphs.
    Note: To get these, I used the commands


    Due Wednesday 4/11 at 9am

    Exam 2 - In Class Portion

    No Reading Questions Today!


    Due Friday 4/13 at 9am

    Section 13.3: Double Integrals in Polar Coordinates

    E-mail Subject Line: Math 236 Your Name 4/13

    Reading questions:

    1. Why might we want to convert a double integral from rectangular coordinates to polar coordinates?
    2. When we use iterated integrals to evaluate an integral in polar coordinates, what is dA?


    Due Monday 4/16 at 9am

    Section 13.4: Surface Area

    E-mail Subject Line: Math 236 Your Name 4/16

    Reading questions:

    1. Give a real-world example where you would want to compute the surface area.
    2. After partitioning the region R, what objects are used to approximate the surface area over each subregion Ri?
    3. Where does the cross-product come in?
    4. What formula from earlier in the semester does the formula for surface area remind you of? Why might these two quantities have similar formulae?

    Reminders:


    Due Wednesday 4/18 at 9am

    Section 14.1: Vector Fields

    E-mail Subject Line: Math 236 Your Name 4/18

    Reading questions:

    1. Figures 14.3(a) and 14.3(b), shown below, are both representations of the vector field H(x,y)=. Which one is (probably) more accurate?
    2. Suppose the vector field shown below represents the flow of a small portion of a river, and suppose a leaf were to fall into the water at the point (-2,2). Describe the movement of the leaf.

      fieldplot(f(x,y), x=-2..3, y=-2..3, fieldstrength=maximal(2),color=red);

    3. Compare this behavior with the path the leaf would follow if it fell in at the point (-2,2.5) instead.


    Due Friday 4/20 at 9am

    Section 14.2: Line Integrals

    E-mail Subject Line: Math 236 Your Name 4/20

    Reading questions:

    1. Give two different uses for line integrals with respect to arc length.
    2. If you're evaluating a line integral with respect to arclength, does the orientation of the curve matter? If so, what difference does orientation make?


    Due Monday 4/23 at 9am

    Section 14.2: Line Integrals (continued)

    E-mail Subject Line: Math 236 Your Name 4/23

    Reading questions:

    1. Give at least one use for component-wise line integrals.
    2. If you're evaluating a line integral with respect to any of the axes, does orientation matter? If so, what difference does orientation make?

    Reminders:


    Due Wednesday 4/25 at 9am

    Section 14.3: Independence of Path and Conservative Vector Fields

    E-mail Subject Line: Math 236 Your Name 4/25

    Reading questions:

    1. Why are conservative vector fields so helpful when evaluating line integrals?
    2. Why is Theorem 3.2 called the Fundamental Theorem for line integrals?


    Due Friday 4/27 at 9am

    Section 14.4: Green's Theorem

    E-mail Subject Line: Math 236 Your Name 4/27

    Reading questions:

    1. What surprises you about Green's Theorem?
    2. Give an example of a region R in the plane where Green's Theorem does not hold.

    Reminders:


    Due Monday 4/30 at 9am

    Section 14.4: Green's Theorem (continued)

    No reading questions today


    Due Wednesday 5/2 at 9am

    Section 13.5: Triple Integrals

    E-mail Subject Line: Math 236 Your Name 5/2

    Reading questions:

    1. Why might you need to compute a triple integral?
    2. What is often the hardest part of calculating a triple integral?


    Due Friday 5/4 at 9am

    Section 13.6: Cylindrical Coordinates

    E-mail Subject Line: Math 236 Your Name 5/2

    Reading questions:

    1. What are some of the advantages to using cylindrical coordinates?
    2. What disadvantages are there?


    Here ends the reading for the semester!


    Janice Sklensky
    Wheaton College
    Department of Mathematics and Computer Science
    Science Center, Room 109
    Norton, Massachusetts 02766-0930
    TEL (508) 286-3973
    FAX (508) 285-8278
    jsklensk@wheatonma.edu


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