Weekly Problem Sets
Math 236: Multivariable Calculus — Spring 2018

January and February, 2018

Be sure to check back often, because assignments may change!
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• Description of multi problem sets: my reasoning, procedures, expectations
• Guidelines for Homework Presentation
• Remember: daily WeBWorK assignments as well as weekly assignments
• Work on the problem set throughout the week
• I suggest completing the WeBWorK exercises first
• If you work with others on a weekly problem set,
• in the end, the work and understanding must be your own
• cite your collaborators on specific problems, or at the beginning of the problem set

• Guidelines for using technology: Do not use technology to accomplish the main purpose of a problem. For example, if the problem is in a section on the dot product, you may not use a dot product command to do it for you, or if the problem is in a section on understanding surfaces, you may not use technology to graph the surface unless specifically noted. However, you may use technology to look at a graph if that is not the main point of the problem, or to help with individual algebraic steps of a problem.
• Please come to see me for help or support!

PS 1: due Tuesday January 30 at 4pm

WeBWorK: Covers part of Section 9.1

Handwritten:

Section 9.1: 1a-h, 3, 5, 7, 10, 15, 18, 26, 38
Notes: For 18, make a table of the x and y values without first eliminating the parameter.

PS 2: due Tuesday February 6 at 4pm

WeBWorK: Covers the rest of Section 9.1, as well as 9.2, 9.3, 9.4, and a bit of Section 10.1
For the polar area problems, you may use technology to do the harder integrals
(but cite when you do). The main point is setting up the problem.
Handwritten:
Section 9.1: 50, 66ab
For 50, you may use Mathematica for the sketch portion of the problem,
but if so, be sure to think about why the graph looks as it does

Section 9.2: 4
Section 9.3: 36
Section 9.4: 4
Section 10.1: 1abcdfh, 42, 44, 45
For Problems 42, 44, and 45, sketch traces and identify type of surface
( make it clear which traces you are sketching)

PS 3: due Tuesday February 13 at 4pm

WeBWorK: Covers review of polar coordinates an graphs, Section 10.1, and parametrizing surfaces (relating Section 10.1 to Section 9.1)

Handwritten:

Section 10.1: 10, 43, 46
Section 11.6 (Smith and Minton): 9, 10, 11, 16, 19, 24, 25, 26
For problems 9, 10, and 11, identify the surfaces by eliminating the parameters to find
an equation relating x, y, and z. Instead of sketching by hand, turn in 2 Mathematica
plots for each one, one using ParametricPlot3D to graph what you are given, and another
using either Plot3D or ContourPlot3D (as appropriate) to graph your result. Pay attention
to the differences in appearance between the two each time.

PS 4: due Tuesday February 20 at 4pm

WeBWorK: Covers Sections 10.3 and 10.4

A note on the webwork:
• Problem 10: You may have seen in a previous course that if a force of magnitude F is exerted on an object, moving it a distance of d in the direction of the force, then we can calculate the work done by the force:
work=(F)(d).
If the force vector F moves the object from point P to point Q where F isn't in the same direction as PQ, then I hope you see that it makes sense that work=(compPQF)(d).
But if we use that compPQF=F.PQ||PQ||, this simplifies to the very nice formula:
work=F.PQ.
Handwritten:
Section 10.2: 1, 15, 52, 56
Note: If you are looking at Problem 55 for guidance with Problem 56, be aware
that the answer to 55(c) in the back of the book is incorrect; the correct
answer to 55(c) is <-2+3$\sqrt{2}/2$/2 , -3$\sqrt{2}/2$/2 >
Section 10.3: 1, 2ac, 10, 11, 29, 38
Section 10.4: 1abcdeh, 2a, 15, 18, 20, 38, 54
Note 1: For Problem 54, can Problem 15 help?
Note 2: For odd problems, always come up with your own examples and be sure to
go into more detail than the back of the book does.
Section10.5: 1ab

PS 5: due Tuesday February 27 at 4pm

WeBWorK: Covers Sections 10.5, 10.6, 11.1, and a little of Section 11.2

Handwritten:

None - I want you to be able to get immediate feedback on whether you are understanding this problem set before the exam Tuesday evening.

When studying, remember that in addition to the study guide, you can of course always do additional problems from the textbook

That's it for February's assignments.
Go to the problem sets for March!

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

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