Reddit mentions of A Tour of the Calculus

I am much more familiar after I took the tour.

I've studied from Stewart's Calculus: Early Transcendentals and like it very much. Every page uses colour, it has a lot of pictures for building intuition and tons of examples and exercises. A downside might be the sheer size of it -- I've no doubt covers far more than you need to start a physics degree, and you can't exactly carry it around in your pocket. But it's a handy thing to have on the shelf, for sure.

If you haven't seen any calculus before you might enjoy Berlinski's A Tour of the Calculus, which is a very gentle, conversational introduction with almost no formulae; it can be read in a weekend and should give you a flavour of what calculus is about.

[EDIT: Regarding the exercises in Stewart, it may be worth emphasising that you'll only learn calculus by working a lot of calculus problems. So lots of exercises with solutions are a huge advantage if you're self-studying.]

This is a more casual book but the author is an excellent mathematical writer.

A Tour of the Calculus - David Berlinski

A Tour of the Calculus by David Berlinski is a very poetic introduction to basic calculus, both in its intuitive concepts and its rigorous development through the intermediate and mean value theorems. The whole book paints a very artistic picture of the whole subject, interlacing mathematical descriptions with historical discussions of the founders themselves and anecdotes of the author's own experience teaching the subject. From the introduction:

>Whatever physicists may say, both space and time, it would seem, go on and on; the imaginary eye pushed to the very edge of space and time finds nothing to stop it from pushing further, every conceivable limit a seductive invitation to examine the back side of the beyond. We are finite creatures, bound to this place and this time, and helpless before an endless expanse. It is within the calculus that for the first time the infinite is charmed into compliance, its luxuriance subordinated to the harsh concept of a limit. The here and now of ordinary life, these are coordinated by means of a mathematical function, one of the noble but inscrutable creations of the imagination, the silken thread that binds together the vagrant world's far-flung concepts. Fabulous formulas bring anarchic speed panting to heel and make of its forward rush a function of time; the wayward area underneath a curve is in the end subordinated to the rule of number. Speed and area, the calculus reveals, are related, the revelation acting like lightning flashing between two distant mountain peaks, the tremendous flash of light showing in the moment before it subsides that those peaks are strangely symmetrical, each existing to sustain the other...
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>The dryness of this description should not obscure the drama that it reveals. Of all the miracles available for inspection, none is more striking than the fact that the real world may be understood in terms of the real numbers, time and space and flesh and blood and dense primitive throbbings sustained somehow and brought to life by a network of secret mathematical nerves, the juxtaposition of the two, throbbings on the one hand, those numbers on the other, unsuspected and utterly surprising, almost as if some somber mechanical puppet proved capable of articulated animation by means of a distant sneeze or sigh.

It really is a fantastic piece of writing, mathematical or otherwise.

On the textbook side of things, Strogatz' Nonlinear Dynamics and Chaos is an excellent read. It is a textbook, with exercises and technical descriptions, but it reads surprisingly casually. I just read it front to back like a regular book and enjoyed the whole thing immensely.