In this book, many broad topics which constitute the cornerstones of a basic calculus curriculum are discussed less formally but in engaging depth. Ideas such as the Fundamental Theorem of the calculus and epsilon-delta formalism are given a context and an overview that - for me - really enhanced my understanding of the development of calculus and how it has evolved, been applied and expanded over time.
I would recommend this book as a helpful supplement to a standard calculus class for its contribution to motivation of the subject and for its lucidity. This is a very valuable book for enrichment purposes and could really help in making a class many students find very tough, much more enjoyable and rewarding.
This book started out with borderline purple prose but an entertaining way of describing and illustrating calculus. It was a nice connection between theory and real world, with forays back to the personalities that shaped it. It was slow reading and sometimes a slog, but clear. I do like formulas as "Form of words"
Unfortunately, as his prose grew less purple and he entered into the more difficult areas of calculus, he also focused too much on the formulas while also trying to simplify them, sometimes successfully--sometimes not. I had to go look one theorem up online to confirm why his proof wasn't making sense--he'd either dropped a line of the theorem or simplified it invalidly (mean value theorem says nothing about being 0--just about being a value between a and b). That was the point where the book took a nose dive--I have learned calculus and his dropping steps made it more confusing, and I am unconvinced it would make it easier for anyone except those who skipped those sections (at which point doing it correctly wouldn't change anything).
He did a lot of good things in the book. I enjoyed his class, I enjoyed the biographical snippets (unclear how much is real and how much is artistic license, but it brought it alive). I just wish he'd maintained his ability to connect calculus to the real world throughout the book, rather than every now and then remembering that's what he was trying to do.
I am not sad to have read it, but it took a very long time to get through and I do not think I'd read it again. He is entertaining -- adding in the anti-math listeners' complaints during a proof was fun. Still, hard book and I'm not sure the second half really illustrated anything useful; the first half did a nice job connecting things.
This book is sort of like a condensed Reader's Digest version of a first-year calculus textbook, written by an over-enthusiastic math student turned dramatic actor. Unless you are familiar with the math in the first place, it will be hard to fathom his explanations, and the rest is like sitting through an endless conversation with a drunken grad student trying to impress you with pedantism -- about math, science, history and every other subject under the sun. Blecherous.