One of my favorite books [1], a great little book that my grandfather gave me, is now available on project gutenburg (free ebooks transcribed from old out of print material). Check out their Mathematics Bookshelf.

I’d seen this book recently in the Markham public library. It’s been republished with additions, but I didn’t feel the new author added much value.

It’s interesting to see that this project also makes the tex sources available. Because of that I can include the awesome prologue and first chapter from this text in this post. Check it out. Doesn’t it whet your appetite for more calculus?

# Prologue

Considering how many fools can calculate, it is

surprising that it should be thought either a difficult

or a tedious task for any other fool to learn how to

master the same tricks.

Some calculus-tricks are quite easy. Some are

enormously difficult. The fools who write the textbooks

of advanced mathematics—and they are mostly

clever fools—seldom take the trouble to show you how

easy the easy calculations are. On the contrary, they

seem to desire to impress you with their tremendous

cleverness by going about it in the most difficult way.

Being myself a remarkably stupid fellow, I have

had to unteach myself the difficulties, and now beg

to present to my fellow fools the parts that are not

hard. Master these thoroughly, and the rest will

follow. What one fool can do, another can.

# To deliver you from the Preliminary Terrors

The preliminary terror, which chokes off most fifth-form

boys from even attempting to learn how to

calculate, can be abolished once for all by simply stating

what is the meaning—in common-sense terms—of the

two principal symbols that are used in calculating.

These dreadful symbols are:

(1) which merely means “a little bit of.”

Thus means a little bit of ; or means a

little bit of . Ordinary mathematicians think it

more polite to say “an element of,” instead of “a little

bit of.” Just as you please. But you will find that

these little bits (or elements) may be considered to be

indefinitely small.

(2) which is merely a long , and may be called

(if you like) “the sum of.”

Thus means the sum of all the little bits

of ; or means the sum of all the little bits

of . Ordinary mathematicians call this symbol “the

integral of.” Now any fool can see that if is

considered as made up of a lot of little bits, each of

which is called , if you add them all up together

you get the sum of all the ‘s, (which is the same

thing as the whole of ). The word “integral” simply

means “the whole.” If you think of the duration

of time for one hour, you may (if you like) think of

it as cut up into little bits called seconds. The

whole of the little bits added up together make

one hour.

When you see an expression that begins with this

terrifying symbol, you will henceforth know that it

is put there merely to give you instructions that you

are now to perform the operation (if you can) of

totalling up all the little bits that are indicated by

the symbols that follow.

That’s all.

# References

[1] Silvanus P Thompson. *Calculus made easy*. Macmillian, 1914. URL http://www.gutenberg.org/files/33283/33283-pdf.pdf.