## 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]
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.
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
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
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
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
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
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

### Nutritious Homework

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!