Welcome, please note that the homework and syllabus are linked just below.

The tests will follow closely the material emphasized in the reviews below. The best defense is to understand the homework and lecture examples, meaning you can do them cold without looking at a solution. Most of you will find the test is long so it is important that you learn how to calculate the problems both correctly and quickly. I have also posted the formula sheet that I will provide for you on the test day, you can keep the one I gave you in class and use it to study. You should pay specially close attention to the test format comments.

These solutions are due to your peers and me, mostly me it turns out. We have selected the solution that we believe is most helpful to all and posted it for everyone's convenience,

These are my solutions to some of your homework. I have tried to select at least one of each type of problem you will encounter. These serve as additional examples to those given in lecture. You are of course free to ask me for further clarification if you find my solution to terse. Some of these problems are more advanced than the typical level of this course, I include those problems for your edification and my amusement. I have tried to include little remarks to alert you to the fact my solution is optional (meaning I don't expect you to do it the way I do it, for example anywhere I use the repeated index notation or "Einstein" notation you may ignore it if you like, but you should think about how to do it in your own brute-force way). Generally speaking you may choose the notation that you find most natural, sometimes I will use a notation that all of you find obtuse and obscure. I have my reasons, perhaps some of you will appreciate them. Those things which are "optional" are likely to show up as bonus questions on test ( just a point or two)

Posted below are links to my lecture notes from ma 242. I have tried to eliminate all the errors from the ma 242 material, but it's likely there is something wrong somewhere. If you find an error in the notes somewhere in pages 236-425 and you are the first to email me about it then I will give you a bonus point. Generally, the material in these notes matched up with the text, however, in several places, the text is not as detailed as I would like, so I add examples and discussion. I have intentionally tried to avoid duplicating examples that are given in your text. I do try to follow these notes fairly closely in lecture, modulo questions about homework.

Running tab of errors big and small we find as I lecture:

1.) E4 on pg. 245 is incorrect, should have used A=(0,0,alpha)

2.) on pg. 253 I forgot to insist that skew line could not be parallel. A pair of lines are skew if they are nonintersecting and nonparallel.

3.) In the Proposition on pg. 273 it should be absolute value of dT/dt at time t_o. The theorem I was thinking about said positive curvature to rule out the case of zero curvature.

4.) In the formula for K(t) it should be a |r'(t)| in the denominator, NOT simply |T(t)|.

5.) In E45 on pg. 283 I forgot to put a T and an N on the LHS of those equalities. You can spot something is wrong because w/o modification we would be equating a scalar and a vector, not good.

6.) In E73 on pg. 313 the math is correct for R = 1/R1 + 1/R2, but physically its wrong, we should have 1/R. 7.) In E75 on pg. 315 the last paragraph incorrectly claims <1/sqrt(2),-1/sqrt(2)> is direction for max change in f, we should instead say the unit vector in the <1,1/2> direction gives max change, that unit vector is (1/sqrt(5))<1,1/2>. Likewise the unit vector for max negative change would be (-1/sqrt(5))<1,1/2> which is the unit vector opposite in direction to the gradient at (1,-1).

8.) In E82 in the notes I incorrectly suppose f_xy = 0 at one point on pg. 322. It doesn't change the outcome of the problem, but f_xy = 4 in fact so D=10-4=6 which leads to the same results. 9.) In E173 I forgot to put "rho"^2 in the dV, correct answer is (pi*R^5)/5

These are not required. It is entirely possible to make an A+ w/o ever doing any of these. You may achieve a maximum of 15pts bonus. These are weighed the same as tests. It is much easier to earn these points on the test, but hey this is bonus so don't complain. These are due May 7 at the latest.

These are my course notes from Calculus I and II, somtimes I reference them in the calculus III notes, so there here if you need them.

The Hannah says do your homework early and ask good questions. You can't argue with the Hannah, she's always right.

I have gathered together some simple applications of Maple to aid you in completing your homework. Of course, you can find much more in the Maple help, but this ought to get you started. We can add to this list as the semester goes on with your help. I want to post more very simple Maple sheets that get straight to the point of how to do this or that with Maple. So if you know something else that would be good to add here, email me your idea ( and attach the sheet).

posted below are Maple examples from class, without output.

In this you can see the TNB-frame follow the path that wraps around the donut, the circle is the osculating circle. You can decipher the Maple code to see how my brother cooked this one up, we've covered the requisite theory, you just need to think about the Maple coding to make it all animated and such, you could change the code to do other curves as well.

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Last Modified: 4-24-07