ANNOUNCEMENTS
Math 203 - Fall 2001

1/1/02
The answers to the final are below. Solutions are posted outside Clapp 423. Stop by Shattuck 208 (late mornings are probably best) to get your exam back.
1. (1,1) is a local minimum
2. (a) (2i+j+2k)/3 (b) 0
3. (a) v = 3et i + (2t+4) j ; a = 3et i + 2 j (b) T = (3i+4j)/5 (c) N = ±(4i-3j)/5
4. (a) conservative; potential=x²+2xy+y² (b) 4
5. (a) Figure 3 (b) Figure 1 (c) Figure 2
6. -128 Pi/3
7. (a) 2 Pi (b) 0
8. 81 Pi/2
12/14/01
There will be a review session tonight at 7 in Shattuck 207.
12/11/01
Two Math Department announcements:
  1. You are all invited to the Math Dept end-of-semester party, which is TOMORROW, Wednesday, around noon in 416 Clapp. Sandwiches will be provided.
  2. If you would like to be on the Math Dept email list, please send an email to Laurie Kamins (lkamins@MtHolyoke.edu) and let her know. This request is especially aimed at, but not limited to, those of you who are considering majoring in math.
12/10/01
The final will be given through the exam center, and can be taken during any of the regular exam sessions next week.
12/6/01
You can run the software I used in this afternoon's demonstration yourself! All you need to do is click here, then follow the first link. Since it's written in Java, it *should* work on just about any computer.
12/4/01
Solutions to both midterms have been posted outside Clapp 423. Please remove them only to make copies.
11/30/01
There will be a (fun!) computer demo after class next Thursday (12/6). Pizza will be provided! It's across the hall in Clapp 416, starting at 12:20 PM. Here's a brief description:
Derivatives of functions have something to do with linearization -- they give the slope of the tangent line to the graph of the function. What is the corresponding statement for derivatives of vector fields? In this talk, I will demonstrate a Web-based program, developed by Matthias Kawski at Arizona State University, which allows one to analyze 2-dimensional vector fields, with emphasis on the linear structure that underlies their derivatives. Along the way, we will get to see what the divergence and curl really are, and how they are related to flux and circulation.
11/19/01
Here are the answers to the second exam:
1. -6
2. 16+2*Pi
3. (a) not conservative (b) conservative; g=x3+yz2+x2sin(y)cos(z)
4. absolute max at (1,1) and (-1,-1); absolute min at (1,-1) and (-1,1)
5. a=aTT+aNN, with aT=0 and aN=3
11/13/01 EXAM ANNOUNCEMENT:
On the last problem, the derivative of T is a mess! Find another way to answer the problem.
11/9/01
Here are the figures shown in class today, showing the definitions of cylindrical and spherical coordinates. The corresponding basis vectors are also shown.
Be careful! Our conventions for spherical coordinates are the standard ones used by most scientists except mathematicians. In particular, our conventions differ from those in your textbook. You may use any conventions you like, so long as we can clearly follow your work.
11/7/01
There will be a midterm next week:
Anyone needing special accommodation regarding these ground rules should contact us as soon as possible (if they have not done so already).
11/1/01
The second midterm is tentatively scheduled to be handed out in class on Tuesday, November 13, to be turned in the following day, Wednesday, November 14, at 2 PM. If these times are difficult for you, please let us know as soon as possible!
10/30/01
You can use Maple to plot vector fields! An example from today's class is:
with(plots):
fieldplot([exp(-2*x),0],x=0..1,y=-5..5,arrows=slim,grid=[5,5]);
whose output can be found here. (Note that Maple rescales vector fields so as to produce a nice picture...)
10/23/01
You may wish to consult the schedule for up-to-date information about which sections in the text we are covering on which day.
10/16/01
Here is an example of a function of 2 variables with 2 local maxima but no local minima -- something which is not possible for (continuous) functions of 1 variable.
(The graph shown is z = - (x2-1)2 - (yx2-x-1)2.)
10/15/01
Here are the answers to the first exam:
1. (a) 4 (b) 0 (c) 0 (d) 2k
2. (a) 1.8 °F/ft (b) max: sqrt(5.04) °F/ft; direction: (i+2j+0.2k)/sqrt(5.04)
3. (i+2j+3k)/sqrt(14)
4. (a) dx(i+(5/4)j) (b) -5i+4j (many answers possible)
5. (a) 10 (c) (0,1.1) (d) (0,1.7) (all answers approximate)
10/5/01
There will be a midterm next week:
Anyone needing special accommodation regarding these ground rules should contact us as soon as possible.
The next homework assignment will be due Wednesday at 2 PM; we hope to be able to return it prior to the exam.
10/4/01
The figures shown in class today appear below, drawn using Maple. In each case, the first picture shows the (3-d!) graph of a function z = f(x,y), and the second shows the combined (2-d!) graph of the level curves and gradient of f.
paraboloid: graph gradient
saddle: graph gradient
And here is a 3-d example due to Greg Quenell, showing several level surfaces as well as the gradient for a particular function of 3 variables.
You can find the Maple code which produced this drawing here. You will need to load this file into Maple in order to see the commands; you're browser can be set up to do this automatically (if you have Maple).
10/3/01
The lab originally planned for tomorrow has been rescheduled for Friday. The homework and schedule pages have been revised accordingly.
10/2/01
You should take a look at the first page of §14.3 (page 651).
To be fully prepared for Friday's class, you should draw the contour map of the function h=5000-30x2-10y2, as given on the homework page. You do not need to turn this in. Feel free to use appropriate technology.
9/28/01
Several people did the wrong problem 16 on the homework due this week. The assigned problem was on page 634, not 635! You may still get credit for the assigned problem, by turning it in late.
The homework due next week was incorrectly announced as being due on Thursday, rather than Tuesday. Under the circumstances, we will of course accept homework through Thursday at the start of class. We encourage you to turn in the homework before then, as we have already moved on to other material!
9/26/01
You can use Maple to multiply vectors! An example which computes the dot and cross product of 2 given vectors is:
with(linalg):
v:=[1,2,3];
w:=[2,3,4];
dotprod(v,w);
crossprod(v,w);
Other useful commands are evalf(%); which converts the previous result to an approximate decimal, and restart: which restarts Maple, clearing all previously defined variables.
9/25/01
Examples 3 and 4 in §14.1 are worth looking at.
9/24/01
The first exam will most likely be handed out in class on Thursday, 11 October, due in class the following day, with students expected to spend no more than an hour on it. Please let us know ASAP if you anticipate any problems with these dates.
9/21/01
Good things to read:
§12.5 (examples of level surfaces; catalog of surfaces; but not the last page)
§13.3-§13.4 (the parts about the equation of a plane)
(You should not memorize the equations for the surfaces in the catalog.)
You can use Maple to graph equations! In 2d, you can use the command "implicitplot", for example:
with(plots):
implicitplot(x^2+y^2=25,x=-5..5,y=-5..5);
but in 3d you must use "implicitplot3d", for example:
with(plots):
implicitplot3d(x^2+y^2+z=50,x=-5..5,y=-5..5,z=25..50);
You can use these commands to draw your own pictures of some of the surfaces in the catalog referred to above.
9/18/01
The figures below are taken from today's computer demonstration, using Excel. They show 3 representations of the function 50-x^2-y^2.
The first figure shows a (2-dimensional) table of numerical data. The second figure shows the same data graphically, in terms of colored regions on which the function is nearly constant. The third figure shows a 3-dimensional graph of the function. Think about the relationship between these 3 representations.
9/17/01
The example at the end of class on Friday is well worth going over on your own. Here's a slightly extended version:
Let v=i+j and w=2i. Find both v · w and v × w.
It is important to try to do each of these computations in several different ways. Possibilities include: using the geometric definition, using the algebraic definition, and using the distributive property of (vector) multiplication over addition. Make sure you get the same answer with each method you try!
9/14/01
A copy of the text is now on reserve at the library.
9/13/01
There will be a review session on the basic properties of vectors tonight at 8:30 in Shattuck 207.
9/12/01
Because of the unusual circumstances yesterday, we will accept this week's homework up until the beginning of class on Thursday.
9/11/01
We will not cover §13.2 in class. You may wish to read this material on your own for enrichment.
9/10/01
Where on Earth is Coriander? In the US, some cities from which the magnetic North Pole lies roughly 14° east of the geographic North Pole are: Billings, MT; Salt Lake City, UT; Flagstaff, AZ; Los Angeles, CA. Note that these cities do not lie on a straight line! (What is a straight line on a sphere?) What shape do curves of constant magnetic deviation have? (This is not easy, and certainly not obvious; we're not yet sure ourselves what the answer is!)
9/7/01
We have decided not to collect individual writeups of the group activities, although there will almost certainly be homework questions based on these activities. (The recorder sheet should still be turned in before you leave, but will not be graded.) The grading policy has been modified accordingly. You may also be able to get some brownie points by showing us an activity notebook at the end of the semester, containing beautiful (and correct!) lab writeups.