Date: Sep 21, 2004 11:26 AM
Author: nstahl@uwcmail.uwc.edu
Subject: Re: [CALC-REFORM:3146] Again, with EMPHASIS

On 12/11/96 --- Mark (bridger@neu.edu) wrote:
I might add that the Harvard Consortium materials represent a
step backward in the notation and discussion of function. The
book begins with the absolutely worst definition of function
I have ever seen, and uniformly writes things like "Let P =
e^{-3t} denote population at time t." (Not even P(t).)

***
I have to disagree with that comment. I sincerely wish more texts
would use variable notation like that given above. One of the bad
things we often do in calculus courses is to only use function notation.

There are a lot of situations in the world where variables are more
useful. One good example involves velocity. In important situations
which occur in some of our classes, velocity depends on time or on
height. If we try to write v(t) and v(h) we abuse function notation.
If we write v as v(t) part of the time and as v in terms of h other
times it's confusion city for our students. If we just treat v as a
variable and use the various relations between v and t and h we get
along fine and our students learn valuable skills.

Mathematicians feel it is important for students to learn about
functions It is also important they learn to use variables,
which will be of value in other courses and in later life.
Why not do both? There is plenty of room for both notations in
our algebra and calculus books.

Neil Stahl