But mathematicians found a clever way around the problem:

From the preface of Prof. E. McSquared's Calculus Primer:

BEWARE!

THIS IS A GENUINE CALCULUS BOOK,

Our original idea was this: if we could find characters for each mathematical concept in differential calculus and set them all to work, the result would be far more lively and involving than the usual textbook trip. What happened along the way was that the characters acquired more life than we had expected and sometimes seem to charge off in their own directions. So, if they lead you astray, go back and re-read what you have already done and try the exercises - we have left room to work them out in the book, and the solutions are given at the end of the book. This is a new expanded version of McSquared's original book. At the end of each chapter you will find new extra exercises and excursions. Although they are not needed to get a sense of what calculus is all about, they will give you more practice and lead you through more limit and derivative theorems.

We hope you enjoy the book. Prof. E. McSquared Admiral Ethalyne R.D. and Piggy Hammy and Duckleen Grover and Alfred and Widget and even Malicious Melvin and many others.

What does McSquared's Primer do?

The Primer introduces calculus stressing understanding of the foundations of calculus and offers a concrete approach to the hardest part of differential calculus. It uses cartoons and analogy to bring the problems of understanding limits alive. It can be used to form a one-semester introduction to calculus, as a supplement in a calculus course or for self-study and review.

Here is a sample on ``Velocities'':

Since differential calculus was originally invented to handle velocities, it's about time we figured out what velocities have to do with derivatives.     To start, suppose a point is moving along a wire. The point has a speedometer to tell how fast he is going. (The speedometer registers inches-per-minute instead of the usual miles-per-hour.) This speedometer is a special custom job that reports velocities, which just means that when the point moves forward, the speedometer calls the speed positive and when the point moves backward, the speedometer reports the speed backward as negative. (The only mathematical difference between speed and velocity (when the motion is in a straight line) is that “speed” is usually considered positive no matter what direction the motion is, whereas “velocity” counts forward speed as positive and backward speed as “negative”.)     We have to figure out what the speedometer will read at any particular instant as the point moves along. First we need some sort of way to record what the point does.     One way to keep track of where the point has been in a rough sort of way is to label its location on the wire at the end of every minute. But this doesn't indicate what happens in enough detail to figure out “instantaneous velocity,” which is what speedometers are supposed to report.     So scientists devised a clever new scheme that records exactly where the point is at every instant of time, not just at the end every minute.

It goes like this:    Put a sheet of graph paper under the wire and move the paper at a steady speed to the left as the point moves up and down the wire. (The wire is held fixed above the paper.) Arrange things so that at the beginning of each minute one of the ruled lines on the graph paper is directly under the wire. Finally, the point now has a pencil to trace on the paper as both the point and the paper move.    Our scientists will now demonstrate what will happen.

Now, when the point stops, a complete record of the motion of the point will be given by the curve drawn on the graph paper. Of course, the curve is NOT the actual path of the point — (remember that the point just moves up and down the wire). But if we pull the paper back so that the line through “start” is under the wire, we can use the traced curve to find out exactly where the point was at any particular time during the experiment.       For example,to find out where the point was at 2½ minutes, go straight up to the traced curve above 2½ and make a right angled turn over to the wire. We will end up exactly where the point was at 2½ minutes.     So we can use the traced curve as the graph of a function whose arrows start at any particular time and end up pointing to the position of the point at that particular time. Call this function p(t): it reports the position of the point as a function of time.     Now that we have the function p(t) to provide a record of where the point has been, we ought to be able to figure out how fast it was moving at any particular time along the way. Try the end of the second minute: what was the speedometer reading as the point moved past p(2)=10? To answer this we first need a closer look at what “velocity” means.     Velocity is described here in terms like “ 3 inches per minute” instead of the usual “miles per hour.” The usual formula linking distance, time and velocity is (velocity)×(time) = (distance) or, equivalently, but these formulas only work if the velocity is constant.     But if we suppose that the point speeds up and slows down and even reverses direction as he moves along, the formula doesn't work any more. .

And so on and so on...

Another example?

Prof. McSquared and the team visit MIT!

Click here to see a press release from IAP '79.

Here is the Table of Contents.

If you want to know what this is all about

To order copies,

To find a local bookstore, check

ISBN: 0-9714624-0-2

Written by Howard Swann and John Johnson

Japanese Edition: 1982. Spanish Editions: 1981 and 2006.

If you order directly from the publisher, copies are $24.95 + $3.00 shipping; three or more copies are shipped free. Send e-mail to or write Dyer and Swann Publications, 1675 Weston Road. Scotts Valley, CA. 95066.

Over 53,000 copies sold. There are 264 pages.

Check McSquared's web site.

REVIEWS:

• From Alan Sherlock, The Times (London) Educational Supplement:

Incredible! was my first, disbelieving, reaction to this unique book. Having read it through again, I repeat - incredible...Throughout the authors have lavishly spread their humor...the mathematics ideas are extremely well and accurately presented...the main achievement is in the exceptionally understandable treatment matching the rigorous mathematics. Highly recommended.

• From the American Mathematical Monthly:

An energized fantasy world...not just for those who have been educated on a diet of cartoons, but for any beginning student who needs help dramatizing mathematical arguments...it will delight both young and old. Calculus will just never be the same again.

• From Martin Gardner, Author of the `Mathematical Games' column for the "Scientific American" as well as many books on Science, Mathematics Criticism and Philosophy:

The calculus book looks great. There has never been anything like it. Lots of non-mathematicians and non-scientists would like some insight into calculus... and wouldn't be frightened by this book the way they are by the usual calculus text.

• From Stuart Jay Sidney, American Scientist:

The first of two surprises in this extraordinary calculus book is the successful comic book format. The second is the fact that the book is not a superficial popularization; rather, it is an in-depth exploration of the basic ideas of differential calculus... The book should be a superb supplement to a calculus or precalculus course.

• Here are a couple of reviews that AMAZON has collected:

SAVED MY CALC GRADE