Subject: Math 280 homework 

Monica

Good question. I am glad you asked it.

>I've been toiling over Wednesday's homework and I'm having some trouble
>with problem 2, which gives us a few equations, a point, and tells us to
>find, in the case of a,  d(z,w)/d(x,y).  Now, I understand the chain
>rule and differentials and using matrices to find d(y1...yn)/d(x1...xn).
>However, the answer to the problem is just a number.  Is this number the
>determinant of the matrix we end up with after calculating all of the
>partials?  I mus thave missed something, becuase I was under the
>impression that the answer would be in maxtrix form.  Any helpful tips
>would be appreciated.

The problem is (as so often) notational. (Let \d mean "partial"). When 
Kaplan writes 
              \d(z,w)
              ------
              \d(x,y)
he does mean the determinant of that matrix, but we shouldn't. 
His is the "old way" and it prevents Kaplan from developing a useful 
notation for the "total derivative" (an equally obsolete distinction from 
the "partial derivative.") So, in our course we will always say 
"determinant" when we mean it to be the determinant, unless, of course,
it is obvious (?!) what we mean (i.e. when we forget the distinction.)

The difference becomes acute when the Jacobian matrix is rectangular
(i.e. not square) then we can't take the determinant (although we can
always take all possible determinants.)


Subject: math280

Ani

You write:

>My name is Ani.  I am in your 11 o'clock (MWF) Math 280 class.  I am
>having a lot of trouble with the homework that is due Wednesday (2/3).  I
>was wondering if I could come in sometime tomorrow (2/2) between 2-4pm and
>look over it with you.  Thank you.

It would be much more useful if you could be more specific about what problems
you have. I prefer to deal with course questions by e-mail because it is more
efficient, and you get your answer quicker (usually). Also, my schedule fills 
up several days in advance of an event, and walk-in office hours are impractical.  
That is why walk-in office hours have been abandoned by most businesses and 
professions. 

However, you can check 3-4794 which is my office, and rolls over to 3-5565 (if
my office mate does not answer the phone), the latter being the grafiXlab.
So check if I am in one of those places between 2 and 4 tomorrow. If so, you
are welcome to stop by.

Please note that the Mathematics department offers tutoring service for Math 280
from 7-9pm, Mon-Thur, in Rm 8, Illini Hall.

G.Francis