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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• Re-read the description of multi problem sets, to learn or remind yourself of the reasoning, the procedures, expectations of how you'll work on them, etc.
• You are always responsible for daily WeBWorK assignments as well as for these weekly assignments.
• If a weekly assignment consists of both WeBWorK and handwritten exercises, it is a good idea to complete the WeBWorK exercises first, both because you'll be able to learn from the feedback that WeBWorK gives you, and because usually many of the WeBWorK exercises will be at a more introductory level than the handwritten exercises.
• Remember - for the handwritten exercises, follow the Guidelines for Homework Presentation.
• Work on the problem set throughout the week.
• Each weekly problem set will be due at 4pm Thursdays unless otherwise noted.
• If you work with others on a weekly problem set,
  • remember that in the end, the work and understanding must be your own.
  • you must cite them on specific problems, or at the beginning of the problem set.
• Guidelines for using a graphing calculator, Wolfram Alpha, or Mathematica: 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 calculate the dot product; if the problem is in a section on understanding surfaces, you may not use technology to graph the surface .... unless the problem instructs you to use technology.). However, you may use it 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!

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 10.1

Handwritten:

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:

• 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_PQF)(d).
    But if we use that comp_PQF=^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

Handwritten:

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