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| Marc Corluy |
| Department of Mathematics |
| University of Connecticut |
| 196 Auditorium Road |
| CT 06269, Storrs |
| corluy@math.uconn.edu |
| Lecture Notes Accompanying the C.E.P. Course on Calculus - Summer Intersession 2003 |
Preface
The first thought that quite understandably comes to mind when seeing
these lecture notes is ``Why?". Indeed, there is a multitude of calculus
books on the market. You have the good, the bad and the ugly. They come
in hardcover or paperback and range from affordable over pricey to
downright budget-sinking. And that is just for the English speaking market.
Do I honestly believe that none of these books is any good? Of course not.
The main motivation for me to write these notes is to give a very concise
overview. Every self respecting publisher these days will only consider
letting a calculus book roll off the presses if it has at least four hundred pages.
Every edition, a few dozen pages is added and before anyone (including the author,
I fear) realizes it, the book measures a grand total of 
pages and
costs over a 
. Furthermore, the baffled student (and more than just one
instructor) is intimidated by the sheer volume and the fact that the memorization
of about 300 formulas seems to be encouraged.
These notes are not even seventy pages, and yet give a relatively complete overview
of single variable calculus. For every new concept, a few examples are discussed
to give some intuitive understanding of this new concept. In most cases, if a
theorem is stated, it comes with a proof, yet the proof itself is not a necessity
to comprehend what follows after ``Qed". So proofs could be skipped during a first
reading. ``First reading" of course implies that there has to be a second, and a
third and so on.
The slenderness in volume, of course, comes with a price. Some of your favorite
subjects (and mine) have been skipped: there is nothing at all in
here on implicit differentiation, the inverse function theorem is not even mentioned,
and the myriad of existing integration techniques are only briefly discussed on
about two pages. And that is only the tip of a gargantuan iceberg.
This is unfortunate but not tragic; further exploration is needed and nobody ever
mastered mathematics by reading mathematics. Mathematics is mastered by
doing mathematics.
Yet these few pages are a good starting point to familiarize yourself with some
of the key ideas of calculus. All the rest is ``just a bit of fiddling around with
expressions".
This text has been typeset using the LATEXsystem (with several packages: amssymb, latexsym, amsmath, epsfig, wasysym and amsthm). The function plots
have been generated by Maple VIII and then edited using a handy graphical program
called ``The Gimp". All software used ran on a Linux system with Gnome and KDE
facilities.
At this point, I would enjoy thanking my proofreader Gabe Adamek.
Without him, a couple very nonsensical claims would still have been around on
these pages. I would also like to thank Andrea Lewis for giving me the freedom
in this program that enabled me to express my own peculiar tastes in calculus.
Finally, I feel indebted to Hector Honvoh for his friendly
hospitality with which he has let me invade his office, hug his terminal for hours
on end and spread calculus books, software manuals and empty bottles all
over the place.
| Happy Calculations, |
| Marc Corluy, |
| Storrs (Connecticut), |
| Summer 2002 and 2003 |