Calculus with Analytic Geometry

I have a big, dirty secret: I needed three tries to get through calculus. Needless to say, I went through (or at least started) three calculus books. The third of these was Simmons' first edition of the current volume. Dr. Simmons takes a historical approach to the material, following discovery after discovery. While today we define the derivative in terms of the limit, this definition (and the delta-epsilon proof machinery beneath the limit concept) came after the geometric notion of the tangent of a curve. I found it enormously helpful to know where I was going before I started. And why not? The great mathematicians that built the rigorous foundations beneath the calculus all knew where they had to end up. One other topic that Dr. Simmons enjoys is arithmetic series. This topic unfolded like a flower during its presentation. As I moved into computer science, this provided valuable background to some of the iterative methods of calculation I was exposed to. I might have a different perspective, though; George Simmons was my Calc 2 prof :-)

When I was a freshman in College, a friend of mine showed a book. As I was taking Calculus I simply took it at hand and started to read it. I was surprised because the explanation wasso clear and the text was so well written and in many ways very artistic. I bought it and this book helped me very much. It covers the genesis of calculus, the very basics of limits and function, introduces differential equations, it is very precise on describing differential and integral calculus, it gives you a solid knowledge of Analic Geometry, it is a very good guide to series and my favorite area is more than 1 dimension functions.Its exercises vary from those which teach you the way of thinking through those very hard ones that simply grant that you got it all.One of the best comments I ever read in a book for Enginneers was one that the author made about solving non linear equations.I can't remember literally but it was something like "you should try to solve this non-linear equation using your intelligence, yet sometimes you won't really find a solution". That comment for a Math book is such a evolution.Apart from the Math issues, the author has a deep knowledgeof Phylosophy of Science and its story. Simply one of my 3 favorite technical/ science books ever.

Speaking as an average math student, I found Dr. Simmons' book to be the best "read" of any text out there. The book's writing style was excellent, the example problems were quite helpful, and the appendicies were terrific-- especially the biographical sketches of history's mathematical greats. Those made for a pleasant break when the rigors of infinite series or double integrals took their toll!On a technical level, the book is as solid as any out there, and does a fine job of covering two semesters' worth of calculus. From derivatives to gradients, it's all in there.

While it is true that Simmons advocates leaving off the absolute value sign when integrating 1/x dx, and even assuming he got one problem wrong involving this, to dismiss the entire book as "rubbish" and to recommend "avoiding [it] like the plague" is completely unfair and totally out of proportion. Furthermore, claiming that it's "confusing" to even introduce the idea of the derivative before a formal definition of a limit is given is also unfair. There's absolutely nothing wrong with providing students with this kind of motivation, and you really don't need a formal definition of a limit to understand the concept. Having a correct and intuitive understanding with a minimum of prerequisites is helpful and an admirable pedagogical goal. [In fact, a classic calculus text (the two-volume set by Tom Apostol) even treats integration before differentiation (and limits), and it's completely correct and clear.] I trust that the fact that every other reviewer gave this book extremely high praise will give students the confidence to read and use this text to learn Calculus in an ideal way.

A brilliant book, I say. I have not seen anything in its class to date. Classy intros to just about everything, interesting notes on "genius" mathematicians, fab diagrams, lots of juicy, juicy problems - make this a very likable book. The problems are graded, and there are enough to satisfy any level of intellectual curiosity. Can be used by the beginner, as well as the more prepared student - it's lucid all through, and of course, intensely challenging. Overally, worth every unit of currency!