But they also understand that they are getting the real thing, that they are being treated as intellectual adults. Students find it very hard, as one might expect. I have used this text for the Honors Calculus course at Colby. (His Calculus on Manifolds is, of course, a classic, but it is so terse as to be impenetrable for most students.) There is no multivariable calculus, which is a pity I'd have loved to see what Spivak could do with that at this level. If you want a calculus textbook that does everything honestly but gently enough so that good first-year students can follow it, this is the one. The suggested reading list has not, alas, been updated, with the result that it now has a slightly antiquarian flavor: some of the books are out of print, and some, like tables of integrals, are best replaced by appropriate software tools.īut the core of the text is still the same. Beyond that, there are very few changes, mostly corrections of small mistakes. This was, of course, one of the first applications of the calculus, and it is still one of the most impressive ones. Spivak has added, in particular, a careful account of how one can deduce Kepler's laws of planetary motion from Newton's laws of physics. This third edition is better than the one I read. The treatment of power series also stuck to me, with the result that I've been a fan of series ever since. His chapter on integration in finite terms is another I remembered, and especially problem 7 in that chapter (described as "Potpourri. Spivak's comment that "mathematicians like to pretend that they can't even add, but most of them can when they have to" (on page 179) stuck in my mind. It will give you a measure of Spivak's impact on me to note that I took quite seriously the annotated suggested reading list given in the back, sought out many of those books, and even managed to read some of them. I even read, with some small level of understanding, the sections on complex analysis and the explanation of Dedekind cuts. I read the whole book, making my way far beyond what we had covered in class by that point. this was calculus as an intellectual adventure, deep, compelling, and beautiful. (There are lots of very hard problems instructors will be glad that there is an answer book.) But Spivak's account of what Calculus is all about, his careful but precise account of the theoretical underpinnings of the material, his chapter on the "hard theorems" (the ones that require an understanding of the completeness of the reals), his pictures, even his asides. OK, I'll admit that I wasn't doing all - or even most - of the problems. I remembered the name, bought the book, took it home, and set to reading it. It was definitely in soft covers, perhaps an edition for sale in third world markets. But the name stuck in my head.Ī couple of months into the course, I was trolling the aisles of my favorite bookstore, and saw there a copy of the book. I didn't buy a copy, because I was fairly happy with the notes and with the books I already had. The references were a variety of books that our professors felt could be consulted with profit. The notes, prepared by one of the teachers, were small booklets (probably mimeographed - remember that?). At that time, we didn't use a textbook instead, we used references, and we used notes. I first studied calculus during my first year at the University of São Paulo, in Brazil. Got that? If any of you want to champion some other book, you're itching for a fight. This is the best Calculus textbook ever written. OK, boys and girls, listen up, because I'm only going to say it once:
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