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... I'm now
trying to do the 1st problem and I might be doing something wrong
here. everytime I simplify the magnitudes I get these weird things
with "csgn"'s and "conjugate"'s in them. It doesn't look very simple
to me, I don't even know what those are (or am I supposed to?).
Could you help me out a little?

ps- isn't there any easier way to get the magnitudes of these vectors
other than just writing the whole thing out?

My answer:

huh. try "help(csgn)" and see what it says. if you wish, i will
interpret a bit: maple thinks that things are as general as pssible
UNLESS you tell it otherwise. so for algebraic "things" it tends to
think that they are COMPLEX. we aren't supposed to talk too much about
complex numbers to you, but it isn't too hard to inform you that a
complex number has TWO square roots in general (just as +2 and -2 both
square to 4) and that there's no simple way to decide which is the
"correct" one.

if you type the following sequence of commands, you may get some idea
of what maple is capable of and what it is NOT capable of:

csgn((w^2)^(1/2));

assume(w,real);

csgn((w^2)^(1/2));

the first line should return exactly what you typed in, that is,
csgn((w^2)^(1/2)) because maple is unable to decide what you wanted,
and hence will just echo back what you typed. the second line tells
maple to (guess what!) ASSUME that w is real (not complex). then the
answer to csgn should be different.

this should help you at least understand what the answers are, i
hope. ...

in answer to your p.s.: i think that the sqrt of the dot prod is
probably the simplest way to get the magnitude of a vector in
maple. there are other ways, and we can look at them together
sometime if you would like and have the time.

assume(q,real);

csgn(q/sqrt(q^2));

assume(q>0);

csgn(q/sqrt(q^2));

then you'll get some interesting (well, not too interesting) answers. you'll get some enlightenment about how maple handles questions about absolute value (or doesn't!).

professor, i wanted to know if section 12.7 will be included in friday's exam. you covered it yesterday in lecture but i noticed that the syllabus lists only up to 12.6 for the exam. also, the homework problems assigned to us are good practice but once in a while they don't completely cover the material taught in the lecture or all of the material covered in a section. should we assume the test questions will not be limited to the kind of questions you assigned for homework?

Most of my answer:

good questions. i intentionally scheduled the exam for the day it is. i try VERY hard NOT to test material given in a lecture immediately before an exam. i believe (i hope) that i announced this in class. the review problems handed out cover the material up to gradients, as i had intended.

the test questions: well, you do have access (through the web) to an ACTUAL exam i gave to a math 251 class last semester. the best advice i have as to the kind of exam i'll give is to glance at that. certainly the type of exam is going to be influenced by my approach to the subject -- that's no surprise. comparison to problems you people have to work out yourselves, however, is more difficult. a significant portion of the test will NOT be like the very simplest textbook problems. at the same time, a significant portion of the test will not be like a complete one of the workshop problems. the former is perhaps too easy, since i hope that everyone can find the first partial derivatives of x^4 - 3y^2. the latter is PERHAPS not too hard when looked at in the right way, but sometimes the workshop problems are phrased in a complicated fashion, and they sometimes require rather non-routine thinking. an exam is primarily a measuring instrument, and only very secondarily a "learning experience". if i measure a quantity, i want to make sure that my measuring "tool" has appropriate capacity. (huh? i don't measure mississippi river flow in teacups, or weight of molecules in tons.) so a test i give will mostly be rather routine problems. i dislike surprises on exams.

this is all too abstract. please look at the exam i gave. i don't think i'll give the same exam, but it should be similar in level and spirit. i hope this helps. please let me know.

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