Weekly Problem Sets
Math 236: Multivariable Calculus - Spring 2016
February, 2016
Be sure to check back often, because assignments may change!
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PS 1: due Thursday February 4 at 4pm
WeBWorK:: Covers Section 9.1
Note: For Problem 4, write your answer in the form <x(t), y(t)>Handwritten:
Section 9.1: 1a-g, 5, 7, 10, 15, 18, 26, 38, 50, 66ab
Notes: For 18, make a table of the x and y values without first eliminating the parameter.
For 50, use Mathematica to see what the graph looks like; include a print-out or sketch.
See the OnCourse - InClass Displays - 1/29 PS 1 Mathematica Tips for how to use Mathematica.
See public webpage for multi (link at top of OnCourse) to see how to download Mathematica.
PS 2: due Thursday February 11 at 4pm
WeBWorK: Covers Section 10.1 as well as some of Section 11.6 from Smith and Minton (available through OnCourse)Handwritten:
Section 10.1: 1abcdfh, 42, 44, 45
Note: For Problems 42, 44, and 45, sketch the traces
(showing work as to which traces you are sketching)
and identify the type of surface.The following problems have been moved to PS 3 due to snow storm on 2/8:
Section 11.6 (Smith and Minton): 9, 10, 11, 25
Note: While you don't need Mathematica to do any of these
problems, if you'd like to look at the surfaces, go to
OnCourse - 2/5 - PS2-3DPlots for examples to follow.
PS 3: due Thursday February 18 at 4pm
WeBWorK: Covers parametrizing surfaces (relating Section 10.1 to Section 9.1) and Section 10.1Handwritten:
Section 11.6 (Smith and Minton): 9, 10, 11, 25
Note: While you don't need Mathematica to do any of these
problems, if you'd like to look at the surfaces, go to
OnCourse - 2/5 - PS2-3DPlots for examples to follow.
Section 10.2: 1, 4, 6, 15, 52, 54, 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 >.
PS 4: due Thursday February 25 at 4pm
WeBWorK: Covers Sections 10.3 and 10.4
Some notes on the webwork:Handwritten:
- Two of the problems were written in a way that made it impossible to edit them.
- Problem 2: This problem uses different names for concepts we've learned, plus one related concept we didn't cover in class.
- the scalar projection of b onto a=the component of b in a's direction
- the vector projection of b onto a=the projection of b onto a as in your text and in class
- the orthogonal projection of b onto a=the vector component of b orthogonal to a, b_{⊥}.
- Problem 5: 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.
- There are two ways to compute the distance from a point to a line that use concepts we've learned this week. I'd like you to try both (one is makes more intuitive sense, but involves more steps; the other result is just a formula but has fewer steps).
- Problem 4: Use that process described in 10.3 Example 4.
- Problem 10 Use the cross-product method described in class
Section 10.3: 1, 2ac, 10, 11, 29, 38, 40, 54
Note: In Problem 40, diagonals go through the center of the cube
Section 10.4: 1abcdeh, 2a, 15, 18, 20, 38, 54,
Note: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.
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