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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).