Jochen Denzler
Visiting Asst Professor at the University of Notre Dame during
the academic year 2000/2001
The absolutely outrageous CALCULUS IS COOL webpage
Warning: this material is for a mature calculus audience, which is
why you won't find anything like this in your textbook. Viewing
of material beyond the required textbook style material may lead
to a Math addiction and to a condescending attitude towards your
textbook. It may even impair your ability to get drunk
[assuming you are of legal age], by giving you something
much cuter to do.
The author of this web page assumes no responsibility for missed exams
due to excessive stimulation of thoughts about calculus.
Disclaimer: Views, jokes or saucy remarks are my private responsibility and
shall not be construed as an official statement of the University
Second disclaimer: Just to avoid misunderstandings by a casual observer:
this web page does not contain R-18 rated language, because
it is for a mature audience only.
Texts intended to help mastering material
- Tidbits on hyperbolic functions; in preparation
- The art of integration - part 1 - mainly algebraic reduction to
standard integrals.
[FIXED TYPO line 2 page 3 of that document: corrected version
available here since Feb28, 2:15pm]
Download as pdf-file
or as dvi-file
or as ps-file
A manuscript in informal classroom language, interspersed with
questions, problems and suggestions for self-study, together with
the textbook, and for repeating lectured material.
- Integration by pArts - the second part of the art of integration.
Download as pdf-file
or as dvi-file
or as ps-file
Comments and additions to the textbook's
chapter on this; in particular strategy and orientation.
Similar style as before. Contains joke on log cabins (enhanced
version, don't think you know the entire joke already!)
What's wrong with my proof that 0=1?
- Partial Fractions
Download as pdf-file
or as dvi-file
or as ps-file
A systematic approach covering the most general case of partial
fractions. Efficient calculation for the simpler cases. Some
problems, standard and tough ones. Also solution to the '0=1' paradox
posed in previous manuscript; and solutions to the problems.
DON'T rush to the solutions right away. Try them under exam
conditions (but without time limit), or, if unsuccessful,
with notes, first!
[FIXED TYPO at top of page 5 of that document (trash expression
removed from formula): corrected version
available here since Mar 27, 6:25pm]
- Trig (and hyp) Substitutions
Download as pdf-file
or as dvi-file
or as ps-file
Exploring the analogy between derivatives of inverse trig an hyp
functions on one side, and the trig or hyp substituions to be used
for getting rid of certain square root expressions on the other side.
Also giving a detailed discussion of why the tangent(half-angle)
substitution works, and of the tangent(full-angle) substitution
not covered in the textbook. Four examples discussed thoroughly with
various substitution options. The actual calculations are omitted, but
intermediate steps are given: you can harvest practice problems here.
They are a bit more involved than exam problems, however.
- Series
Download as pdf-file
or as dvi-file
or as ps-file
Unlike the integral manuscripts that covered more than the textbook,
this manuscript cannot be taken as a replacement for certain
textbook chapters. I only thought to stress a few particular points
that I feel are not prominent enough in the textbook.
- Retrospective on some features concerning series
Download as pdf-file
or as dvi-file
or as ps-file
Convergence tests for series is the core part of this. Plus some
stray remarks, namely about Picard's method (not so important, but
to clear up some confusion) and a historical erratum from the
textbook.
- The Joy of Power Series
Download as pdf-file
or as dvi-file
or as ps-file
This unifies the chapters 8.6 and 8.7 of the textbook and gives some
extra material. Next to a practical approach of calculating with
power series, you will see the Mount Rushmore of 1st year calculus
and learn the difference between a tail dog and a mouth dog.
Bonus track
In case you
don't know: A bonus track session, unlike a help session, contains
material not covered in the exam, but uncovering the spirit of
material covered in class.
-
The floating beam: a bonus track on centers of mass This is
only the abstract of the bonus track sessions (which contained
voluntary material, being worked through together with students
of my class interested in that kind of adventure).
-
You Can Count On Power Series! A bonus track that explains you
one example and shows you another one (with some details omitted)
how power series can actually help doing such apparently simple minded
things as counting!!! (No, you won't need this for the course, but
if you want some training how to multiply power series, then here
you have it as cute as it gets.) --- Oh, about counting,
here is a joke that mathematicians tell
occasionally.
- May be continued with other bonus tracks, time permitting
Right now, there is nothing set up to grade or credit the nutritious homework.
Everything on the Calculus is Cool webpage is experimental, deliberately
not the way things are usually being done. Therefore, if you expect
'immediate positive reinforcement' for doing it, I regret that it isn't
available. Personally, I think reinforcement is for lab rats; - humans need
appreciation, love, and inspiring thoughts. But it will take a while until
this distinction gets more widely appreciated.
However, I wouldn't invest all the time in setting this up, if I didn't
believe sincerely that it will help you in getting along better with
the material.
Calculus is the creation of 2-3 centuries, it IS NOT simple.
However, oversimplified calculus is even more difficult!
Follow the link in the headline.
Last modified:Apr 23, 2001