ANNOUNCEMENTS
MTH 254H — Fall 2013

12/9/13

So far as I am aware, our exam remains scheduled at the original time and place, namely 12:00–1:50 PM in Wngr 275.

The announced changes to the group final for MTH 254 apply only to the regular course, not the honors sections.

12/8/13

Below are some Check Your Understanding questions from the Hughes Hallett text. In each case, decide if the given quantity is a vector, a scalar, or undefined, assuming that u, v, and w are vectors.

v·w

v×w

(u×v)·w

u×(v×w)

(v×w)/(v·w)

(v·w)/(v×w)

12/6/13

During this afternoon's review, several students and I came up with the following list of course topics:

Multiple Integration

• Rectangular coordinates (dA=dx dy; dV=dx dy dz);
• Curvilinear coordinates (dA=r dr dφ; dV=r dr dφ dz; dV = r²sinθ dr dθ dφ)
• Limits, and the regions they correspond to;
• Order of integration, and how to reverse the order;
• Interpretation; chocolate; chop and add.

Partial Derivatives

• Zap with d (df = ∂f/∂x dx + ...);
• Chain rule.

Vectors

• Vector addition;
• Dot product (projection);
• Cross product (directed area);
• Position vector (r=x x+...);
• Velocity;
• Vector equation of line (r=r₀+vu).

Gradient

• Magnitude="steepest slope" (|∇f|);
• Direction="steepest direction" (∇f/|∇f|);
• Perpendicular to level curves (∇f⊥{f=const});
• Master Formula (df=∇f·dr);
• Directional derivative (∇f·u);
• Optimization, including 2nd-derivative test and Lagrange multipliers.

Feel free to email me questions over the weekend, including scanned work if appropriate.

12/6/13

Campus is closed this afternoon.

Class is canceled.

Office hours are canceled.

I will however be at the Beanery (26th and Monroe) from 1–2 PM.

I am willing to make appointments for later in the day (but where?).

Both email and voicemail to my office (x75159) should reach me.

12/5/13

Here are some suggestions for review:

• Go over the midterm!
• Review the following sections in Briggs/Cochran: §11.1–7, §12.1–2, §12.4–6, §12.8–9, §13.1–5.
• Review the following sections in Hughes Hallett, McCallum, et al: §12.1–5, §13.1–4, §14.1–7, §15.1–3, §16.1–5.
• In both cases, do enough "Basic Skills" problems (Briggs/Cochran) or "Exercises" (Hughes Hallett) to feel confident, then try some harder problems. Skip problems that do not seem relevant to the material covered in class.
• The Exercises at the end of each section in the Hughes Hallett text are an excellent skills check, and the Check your Understanding questions at the end of each chapter are an excellent review.

12/4/13

The applet I used today in class to draw Lissajous figures can be found here.

12/3/13

I will hold extra office hours this week, on Thursday from 3–4 PM, and on Friday from 3:30–4:30 PM.

12/2/13

In order to do this week's homework assignment, you will need to know some definitions which we didn't quite get to in class, but which can be found here.

12/1/13

A new section in the online book that discusses constrained optimization, and, in particular, alternatives to the use of Lagrange multipliers, can be found here.

11/29/13

The final will be Tuesday 12/10/13 from 12:00–1:50 PM in Wngr 275.

• The final will be slightly less than twice as long as the midterm
• It will cover material from the entire course, but with an emphasis on material since the midterm.
• The main new topics (roughly 50–60% of the exam) are:
  • vectors & vector functions;
  • gradient;
  • optimization;
• The old material (roughly 40–50%) is described below in the midterm announcement.
• Together, these topics correspond roughly to §11, §12, & §13 in Briggs/Cochran.
• You may bring two 3″×5″ index cards (both sides) of handwritten notes, or the equivalent.
• Other rules are as announced below for the midterm.
• Friday's lecture will be devoted to review. Come prepared to ask questions!

11/25/13

The cross-product applet I showed in class today can be found here.

A similar applet for the dot product can be found here.

11/24/13

The homework assignment due next week is due on Wednesday 12/4.

11/22/13

Here are the two problems I put on the board at the end of class today.

• Minimize the surface area of an open rectangular box whose volume is 32 cubic centimeters.
• Find the points on the curve x²+xy+y²=3 which are closest to and furthest from the origin.

The figure I showed in class today, related to the problem of extremizing xy on the circle x²+y²=9, can be found here.

11/20/13

A new section in the online book that discusses where the second derivative test comes from can be found here.

11/18/13

Here is the extra problem from class today.

You are walking through a puddle whose depth is h=50−2x²−2y² inches, with x, y measured in feet. How quickly is the depth changing if you are at the point (3,4) moving "East"? Moving "Northeast"?

(The answers are −12 inches/foot and approximately −20 inches/foot.)

11/13/13

Lab writeup for Friday:

Write up a short description of your group's work on this week's activity ("A Multivariable Derivative").

• Try to relate your answers to the last two questions about the gradient vector to your numerical computations.

11/10/13

Below are the answers to the midterm. Full solutions can be seen in my office.

1. (a) TRUE (b) FALSE

2. (a) 7(x²+x−y)⁶(2x+1) (b) cos(uv)−(uv)sin(uv)

3. e^−6u(5cos(5u)−6sin(5u))

4. interior of parabola y=x² between y=1 and y=4

5. 7π/3

6. 45

7. 61

8. many answers possible; ∂T/∂x<0, ∂T/∂t>0

EC: 81π/5 grams

11/4/13

Here are some suggestions for reviewing for the midterm.

• OSU's current MTH 254 text is by Briggs/Cochran. Relevant sections are included in the online schedule, namely §12.1–§12.5 & §13.1–§13.5. The Basic Skills problems provide good drill.
• OSU's previous text is by Hughes Hallett. Relevant sections are §12.1–§12.5, §14.1–§14.3, & §16.1–§16.5. The Exercises at the end of each section are an excellent skills check, and the Check your Understanding questions at the end of each chapter are an excellent review; many of the latter are TRUE/FALSE questions similar to the most recent homework assignment.
• Both books are on reserve in the library.

I have posted my handwritten notes about Jacobians here.

11/3/13

Two mathematicians are talking on the telephone. Both are in the continental United States. One is in a West Coast state, the other is in an East Coast state. They suddenly realize that the correct local time in both locations is the same! How is this possible?

Give up? Some hints can be found here.

11/1/13

Lab writeup for Monday:

Write up a short description of your group's work on today's activity ("Partial Derivative Machine").

• When answering question 2, clearly explain which quantities were changing, and which were not.
• Make sure you explain how to use your data to complete the measurement, not merely what data you took.
• Make sure you to indicate where you computed the partial derivative, that is, for what values of the independent variables. In particular, please indicate whether multiple measurements correspond to the desired partial derivative at the same point, or at different points. (We will discuss this issue further on Monday.)
• You do not need to answer question 3, but may do so if you wish. If you didn't take the necessary data, describe what data you would have taken, and what you would have done with it. Is there a relationship between these two quantities?

Some further information about the Partial Derivative Machine is available here.

10/31/13

The midterm will be Friday 11/8/13 in class.

• The main topics to be covered on the midterm are:
  • multiple integration;
  • partial differentiation.
• The exam is closed book, and calculators may not be used.
• You may bring one 3″×5″ index card (both sides) of handwritten notes.
• Please write your exams in pencil or black ink (blue ink is OK).
• Please turn off all electronic devices, such as cell phones and alarms; this also includes personal music players.
• Wednesday's class will be devoted to review. Come prepared to ask questions!
• My Friday office hour right before the exam is canceled. I am available on Monday both before and after class.

10/30/13

Lab writeup for Friday:

Write up a short description of your group's work on this week's activity ("Chain Rule").

• Make sure in each case that you can use one method successfully.
• Provide at least one alternative solution in each case if you can.

10/29/13

The homework assignment due today will be accepted through tomorrow morning, either electronically or slipped under my office door (Kidder 298A).

When submitting assignments electronically, please convert to PDF format, as figures and equations often fail to survive translation between different versions of Word and/or equivalent public-domain software.

10/28/13

Some of you may be interested in this afternoon's physics colloquium, entitled Equipping students to connect multivariable calculus with the physical world. The talk is at 4 PM in Weniger 116.

Further information is available here.

10/27/13

I expect to be in my office before class tomorrow (Monday), from shortly after 1 PM until about 1:45 PM.

10/25/13

The correct terminology for traces is that an x trace is parallel to the x-axis. Thus, for our surfaces, it is y that is constant along an x trace.

In today's lab, the goal was to investigate the partial derivatives that were perpendicular to the trace, not parallel to it.

10/23/13

Lab writeup for Friday:

Write up a short description of your group's work on today's lab ("Partial Derivatives").

• You do not need to write up Part 0.
• For Part 1, make sure to describe how you used the tool, and how you obtained numerical values.
• For Part 2, make sure to provide an explanation, not just an answer.

10/21/13

Today's computer demo used Mathematica, the engine behind Wolfram Alpha.

• You can run Mathematica in the MLC computer lab, located in the back of Kidder 108.
• On a machine running Windows, you can also run Mathematica by browsing to http://osurds.oregonstate.edu, logging in, and starting Mathematica from the Mathematics folder.
• From non-Windows machines, you can use the OSU Virtual Computing Lab (Umbrella) to run a virtual Windows machine, then follow the instructions above. (Yes, this works.)

You can download the demo here; the two examples I showed in class were numbers 1 and 5.

10/20/13

Here are some further sections of the textbook that you may want to read:

• Integration Summary
• Non-Constant Limits of Integration
• Polar Coordinates
• Double Integrals in Polar Coordinates
• Review of Multiple Integration

10/18/13

Lab writeup for Monday:

Write up a short description of your group's work on this week's lab ("The Cone").

• Describe two different ways to compute the volume.
• One of your methods should involve a triple integral. I recommend using cylindrical coordinates.
• Make sure to indicate in each case what dV is, and what the limits are.
• Evaluate the integrals.
• Did your answers agree?

10/16/13

Some mathematical typesetting advice:

• Do include drawings, hand-drawn and on a separate page if necessary.
• Don't break lines in the middle of an equation.
• Use both displayed and inline equations.

Some matheamtical terminology:

• You evaluate integrals, and solve equations.
• You integrate with respect to x, not dx.

10/15/13

I will be in my office tomorrow (Wednesday) from 1–1:40 PM.

10/14/13

You can find out more about the reasons we will use the "physics" convention for the names of the spherical coordinates in our paper:

Spherical Coordinates, Tevian Dray and Corinne A. Manogue, College Math. J. 34, 168–169 (2003)

The short answer is that most students will need to switch conventions at some point during their education, so this might as well be done sooner rather than later.

10/11/13

Lab writeup for Monday:

Write up a short description of your group's work on today's lab ("Double Integrals").

• Did your answers agree?
• Did you change your strategy at any point, either due to conversations within your group or the whole class discussion afterward?

You should be able to complete the homework assignment also due Monday; if you run into problems, bring your questions to class (and do the lab writeup first).

10/7/13

Since we will be scanning all written assignments in this class, please:

• Write on only one side of each page;
• Do not staple pages together;
• Use full-sized paper (8½″×11″), preferably without "chads" (remnants of tearing a page out of a notebook).

You may wish to put your name on each page, just in case.

10/4/13

Lab writeup for Monday:

Write up a short description of your group's work on today's lab ("Integration").

• Were you able to get an exact answer (as opposed to a decimal approximation)? That's not necessary, but provides good practice with log rules.
• It wouldn't hurt to confirm that your second computation really does give the same answer as the first. At the very least, do set up the second solution completely, that is, with all integrals and limits explicitly written down, even if not evaluated.

Are two lab writeups per week too much (in addition to one or two homework problems)? Let's discuss this on Monday.

10/2/13

Lab writeup for Friday:

Write up a short description of your group's work on problem 1 of today's lab.

• The correct title of the activity is "The Heater".
• See the guidelines on the homework page and also here.
• Lab writeups are a relatively small part of your grade; don't stress out now trying to get it just right.
• Good supplemental questions: Where is the window? When is it open? When is the heat on?
• Addressing at least one of these questions will improve your content score.

A reasonable length for your complete writeup is one side of one page, including both the description of what you did and a brief discussion of one of the supplemental questions.

9/30/13

Both Maple and Mathematica are available in the math computer lab in the back of Kidder 108.

Wolfram Alpha is of course also available online.

9/29/13

Online materials suitable for reviewing precalculus concepts can be found here.

9/28/13

Several standard calculus textbooks are on reserve in the Valley Library, including Briggs/Cochran (the current text in MTH 254) and Hughes Hallett (the previous text).

You are strongly encouraged to use one or both of these books regularly as a source of practice problems. The Hughes Hallett text in particular has "Exercises", which are more-or-less routine, "Problems", which are more conceptual, and "Check Your Understanding" questions at the end of each chapter, which are True/False questions that can be surprisingly difficult. See me if you are having difficulty choosing appropriate problems.

9/27/13

Here are some suggestions for improving the presentation of your written work:

• Restate the problem in your own words.
• Use (mostly) complete sentences (with the math included as grammatically correct parts).
• Don't write a book — keep it short and sweet.
• Don't use scratch paper; use blue or black ink (or pencil).
• Don't use a multicolumn format.

The goal of your writeups should be to be able to understand them 5 years from now without any additional information.

Further information is available at the top of the homework page.
The criteria I will use to evaluate written work can be found here.

9/25/13

My office hours are posted on the course homepage. Clicking on the calendar icon on that page will bring up my full weekly schedule, which is also available here.

9/23/13

Make sure you read the note about textbooks, and take a look at the grading policy.

I reserve the right to make small changes to these rules.