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.

A book pathetically lacks of rigorous proofs.

Best math book I've ever read. I learned calc in high school and hated it. Learned it again in college and hated it. Turns out I just hated how it was taught to me. This book fixed that and was a ton of fun to read.

Well, easier. Ha! No, actually calculus is in reach of the common mortal. Don't believe the hype.

Fabulous refresher on all the calculus I learned 30 years ago and have since forgotten. Definitely recommend for anyone who enjoys math and doesn't get to do it in their day job.

A great introduction to calculus. Most explanations are rather simplified, but that's done purposefully by the author to make the book more accessible to beginners.

Although I still don't understand calculus I really enjoyed reading this book. It's fun when someone loves the subject so much. The idea of infinitesimals is much more intuitive to me than limits as well. It made me think of all the abstractions which were equally 'correct' that lost out over the years.

Who knew Calculus could be this much easy?
Damn! I wish I had read this book in my college days. ❤️

Good, this is making a comeback. How refreshing to see that calculus can be taught in 200 something pages instead of the modern bricks. This cuts to the bone and is well written. Its available for free with Project Gutenberg. share it with young people before its too late.

This was a book that I skimmed through, rather than thoroughly digested, not least because much of each chapter consists of worked examples and exercises which I didn't attempt. I studied calculus at school, and used it occasionally at university, but I've not needed it since so this was a trip down memory lane. I was attracted to this book by its title, which struck me as unusual for 1914, when my edition was published, and its contents didn't disappoint. The author does indeed present the subject in a way that is easy to understand, and in a style that is entertaining. As I expected, it brought back memories of learning calculus at school although I don't recall the subject being so clearly explained as in this book. Someone trying to learn calculus for the first time could do far worse than using this work as their primer.

I should emphasise that the edition I read was not the one updated by Martin Gardner, with its new introduction, three new chapters and modernised language. These changes will probably have made it more desirable to the modern audience. Nevertheless the 1914 edition I read, which incidentally I downloaded for nothing from the Internet Archive because it's out of copyright, was very readable and it's antiquated style only served to enhance my enjoyment.

I no longer have the interest or, apparently, the capacity to do calculus. Good book. Disappointed n myself.

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