Welcome to the Svobodny
"I
understand the concepts,
I just can't do the problems"
This
is a commonly heard remark coming from calculus students. This shouldn't
be surprising considering that the concepts of the calculus are simple
and few in number. And yet the technical task of executing these ideas
can be formidable. Although the ideas of infinitesimals and limit (exhaustion)
were used as early as the time of Archimedes, it really took the technology
of functions and analytic geometry for Calculus to emerge in the 17th
century as a powerful discipline for solving problems.
Thus
it is very easy to find yourself reading the text without any difficult
or following along in class nodding your head in agreement with the statements
on the board. However, the proof of your understanding of the Calculus
is your using it to solve problems. There is a very simple way to test
whether you understand the subject (or at least, to what degree you understand):
Can
you solve Calculus problems without consulting the book?
If
the answer is YES, you are making progress. If not, you have to work a
little harder. You must try to find at least 2 hours everyday where you
can be alone with your unsolved problems, until as you find yourself solving
problems, seemingly out of nowhere, Calculus is re-created as your personal
tool.
