Page:Calculus Made Easy.pdf/21



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) $$d$$ 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) $$\int$$ which is merely a long $$S$$, and may be called (if you like) “the sum of.”

Thus $$\int dx$$ means the sum of all the little bits of $$x$$; or $$\int dt$$ means the sum of all the little bits of $$t$$. Ordinary mathematicians call this symbol “the