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Calculus texts



Hi all-
I've come to the conclusion that there are no calculus texts
the hew, even approximately, to the pedagogical lines laid out by Arons
for the teaching of introductory physics. The apparent reason that
teachers can get away with using the clone texts, such as Anton's (which
I used last semester -as sparingly as possible), is that the texts are
full of worked out examples. Students can follow the examples almost
verbatim in doing many of the exercises at the end of each chapter.
The end result is that the students, many of them deficient in algebra
skills, can "satisfactorily" complete a calculus course without understanding,
or even reading, any of the textual material. As for understanding any of
the underlying concepts - forget it!
Students with such calculus preparation find themselves almost
totally lost when they enter our calculus-based physics classes. The
frustration with the math preparation of our students has been expressed
frequently on the physics-l net.
My solution to this problem is to write a "decent" introductory
calculus text. The text would adhere to the principles of:
a unifying theme
less is more
write at the level of the students' understanding
concept first, names later
avoid concepts that are unnecessary to the main theme
introduce concepts only as needed in the development of
main theme
continuous "circling back" and revisiting earlier concepts
including those learned in algebra and arithmetic
short, literate chapters, each dealing with a single principle
idea; each followed by relatively few exercises and problems.
The expectation is that a student will do all of the exercises
(and problems).

At the end of a two semester course the student who completes the
text should be able to apply the first and second fundamental theorems of
the calculus to elementary (separable) problems in one and two dimensions.
The student should also be able to derive the rules of calculus and to
work out complicated, unfamiliar integrals. (Maybe less).
I am looking for one or two people to collaborate on such a text.
An ideal team, I think, would be two physicists (to keep it simple) and
one mathematician (to keep it honest).
Any suggestions?
Regards,
Jack

***********************************************************************
It's 4 A.M. Nazruddin leaves the tavern and walks the town
aimlessly. A policeman stops him. "Why are you out wandering the streets
in the middle of the night?" "Sir", replies Nazruddin, "if I knew the
answer to that question, I would have been home hours ago!"
from "The Essential Rumi"