calculus made easy

NO.1 TO DELIVER YOU FROM THE PRELIMINARY TERRORS
(1) d which merely means “a little bit of.”
Thus dx means a little bit of x; or du means a little bit of u. 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 S, and may be called (if you like) “the sum of.”
Thus ∫dx means the sum of all the little bits of x; or ∫dt means the sum of all the little bits of t. Ordinary mathematicians call this symbol “the integral of.” Now any fool can see that if x is considered as made up of a lot of little bits, each of which is called dx, if you add them all up together you get the sum of all the dx’s, (which is the same thing as the whole of x). 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 3600 little bits called seconds. The whole of the 3600 little bits added up together make one hour.

NO.2 ON DIFFERENT DEGREES OF SMALLNESS