Multivariable Calculus - Problem Sets
    Spring 2013, Math 236

    April, 2013

    Be sure to check back often, because assignments may change!
    (Last modified: Sunday, January 20, 2013, 4:43 PM )

    PS 9: due Wednesday 4/3

    WeBWorK: Covers the rest of Section 12.4, all of Section 12.5, and part of Section 12.6. Do any (partial) differentiation without technology.


    12.4: 35, 38, 39
    12.5: 19, 25, 26
    12.6: 24
             It is still important, in sections 12.4, 12.5, and 12.6,
             that you do not use technology to (partially)
            differentiate. Show work.

    PS 10: due Wednesday 4/10

    WeBWorK: Covers the rest of Section 12.6 and some of Section 12.7.
    Ordinarily, on these sections I assign alot of problems. Because of the exam, I tried to keep the number of problems down ... partly by moving some of the problems I would ordinarily assign to the study guide. So you may notice, between the WeBWorK and the traditional study guides, quite a few problems from these sections.


    None: I want you to know before the exam whether the ideas are all making sense

    PS 11: due Wednesday 4/17

    WeBWorK: Covers the rest of Section 12.7.


    12.7: 24, 36
             Feel free to use technology where appropriate in
             these problems -- for instance, to differentiate,
             or to solve for where a partial derivative is 0.
             Do not use technology that simply does the
             optimization or regression for you. Any technology
             that you use, copy or print out and include with your

    PS 12: due Wednesday 4/24

    WeBWorK: Covers Sections 13.1, 13.2, and 13.4.


    13.1: 28

    Part of the point in sections 13.1, as well as in the two sections below, is that you be able integrate. (You need to be able to recognize whether you should change the order of integration or not, for one thing ... and that requires recognizing whether a function is antidifferentiable.)

    Therefore for all the written problems assigned this week, please antidifferentiate by hand.

    13.2: 18, 26
    In Problem 18, be careful. While double integrals can be negative, the volume between two surfaces can not be: when you subtract the volume under the lower surface from the volume under the top surface, the result will always be positive.
    13.4: 2

    PS 13: due Wednesday 5/1

    WeBWorK: Covers Sections 14.1 and 14.2


    14.1: 30, 32
    14.2: 18, 20, 56, 58
    For problems 56 and 58, work through the problems all the way to the point where you would be ready to integrate, but don't actually do the integration. That is, parametrize the curve, write both f and ds in terms of the parametrization, and substitute everything into the integral (including limits of integration).

    Janice Sklensky
    Wheaton College
    Department of Mathematics and Computer Science
    SC 1306
    Norton, Massachusetts 02766-0930
    TEL (508) 286-3973
    FAX (508) 285-8278

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