- 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!** -
**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=(comp_{PQ}**F**)(d).

But if we use that comp_{PQ}**F**=^{F.PQ}⁄_{||PQ||}, this simplifies to the very nice formula:

work=**F**^{.}**PQ**.

Weekly Problem Sets

Math 236: Multivariable Calculus — Spring 2018

January and February, 2018

**Be sure to check back often, because assignments may change!**

( )

**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 thexandyvalues 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 useMathematicafor 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 relatingx,y, andz. 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:

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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