Martin Gardner

Silvanus P. Thompson

A new version of this classic math primer explains the timeless theories of calculus in a contemporary and comprehensible way, with updated method and terminology, and twenty new recreational problems for practice and enjoyment. 20,000 first printing.

Calculus Made Easy

anjali

This isn't all the other calculus books out there. In fact, this is a very old book (early 20th century) and it's surprising how accessible it is (I would say, more than today's books). The writer is witty and sympathetic at all times (the first chapter is called 'To Deliver You From Preliminary Terrors').

Gavin

Ridiculously clear and friendly and quick. He takes your intuitions about little bits and bigness and leads you to the door of the great machine. Shame there's not one of these for every subfield of maths.
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.

Masterstroke! He takes you into confidence against "ordinary mathematicians", he states it all in things you already know, and he directly addresses your misgivings. The only impediment is the Edwardian prose, which tends to make sentences twice as long as they have to be. I like the style.

You could give this to a motivated 9 year old. And I intend to.

Free and beautifully rendered here.

Arron Kau

Available for free on project Gutenberg as a beautifully typeset PDF, this amazing little book presents the most fundamental ideas of the calculus in a surprisingly approachable way. It's certainly light on rigor, but for an introductory primer,that's not such a terrible thing.

Calculus Made Easy

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