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336 pages, Hardcover
First published January 1, 1910
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... 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) ∫ 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... 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... The word “integral” simply means “the whole.”...
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.
Martin Gardner has updated and revised the latest edition. The sections by Mr Gardner are good but not as lucid as those of the original. This is ONLY because the original is so good.