Customer Reviews

Calculus With Analytic Geometry

5 star:		(19)
4 star:		(1)
3 star:		(1)
2 star:		(1)
1 star:		(1)

 

 

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.

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.

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 was so clear and the text was so well written.

I bought it in the next week and this book helped me very much. Because:

- It covers the genesis of calculus, the very basics of limits and functions.
- introduces differential equations.
- it is very precise on describing differential and integral calculus, it gives you a solid knowledge of Analytic Geometry.
- it is a very good guide to series and ( my favorite topic) multivariable calculus.

Its exercises vary from those which teach you the way of thinking to those very hard ones that simply grant that you got it all.

One of the best comments I ever read in a book for Engineers or science in general was a comment made by author 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". This comment for a Math book is such a evolution.

Apart from the Math issues, the author has a deep knowledge of Phylosophy of Science and its story. Simply one of my 3 favorite technical/ science books ever. I still have the two volumes and once I a while I like to read it.

This book is perfect if you are looking for a book that has a nice balance between theory and application. Theory is presented on an as-needed basis and there is more in the appendix if the reader is so inclined. This was an excellent book for me my freshman year and it has been a good reference for me throughout my math career. It is a nice stepping stone on the way to spivak.

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!

As an adult student trying to earn a degree in electronics by correspondence courses, I have had to buy a lot of different math books to attempt to help learn the concepts, especially the Calculus. I probably own about 10 different mainstream texts of recent years, and find that out of the many, this is the one that helps the most.Simmons makes clear the concepts without being boring or giving you only "Plug and Chug" problems.This textbook is actually interesting to read,and does what a textbook should do: teach you something.Highly Recommended!

I originally learned calculus at OU with james stewart 4th edition, but came to this book through the MIT open courseware readings. I love this book and can't understand why math departments everywhere aren't using this as their text. Simmons' strategy for writing about calculus is unique, and in my opinion the best. He gives quite a bit of history and ties it into physics and the other sciences giving the reader a broad perspective on why the hell it matters and how it came to be. At most state unis, calculus is probably more plug and chug, but if you want a better source of material to supplement your class, buy this book.

This book was used for several years in the first two MIT calculus courses. (MIT has, lamentably, moved to a book published by one of it's own professors.) Simmons' text is the essence of a good text book; it has cogent explanations and figures which clearly illustrate. An introduction that non-mathematicians will understand and mathematicians will still respect. I'm convinced it is the best book available.

Out of the millions and millions of textbooks out there and the thousands I have seen since recently completing grad school and teaching undergrad math for the past few years: I have found that a good book is really hard to find. Further, I was recently recommended Simmons's ODE book for a course & really liked the presentation; thus, I wrote McGraw Hill & asked for a copy any of his other books.

Further, they sent me a copy of his calc book (ISBN 0070576424) and it was a pleasant surprise. A well presented and logically order calc book. This book is not a million pages long nor does it ramble on aimlessly about things that are not necessary to the subject (for which I think many authors just put in to make there books look nice).

Simions did stick with the Late transcendental standard approach, but what I found extremely interesting is that he also pushed the tirg items back also; thus, the part one of this book (basic differentiation / integration) could feasible be used for an applied one semester course clac course ( business clac etc.,), but then on the same note all of the material is there to cover very in depth the concepts of integrating trig functions + some of the applications considered in a regular calc w/ anal geom class. Did I mention that he also has a beautiful appendix that really covers what a limit is ( delta / epsilon stuff) and also has some interesting material on functions that cannot be integrated and advanced convergence test + He has two chapters on series (which is nice because that is truly the backbone of calculus & the students need to focus more on that early rather than being pushed through & then later confused in an advanced calc course ). Then in the later chapters ( multi dim calc) he has many neat applications (derivations Maxwell's equations, Graviton laws, derivation of 3 classic PDE's etc.,) + A nice chapter on Line / Surface integral + Green's & Stokes thrms..

So to me this book has solved my problem: when teaching a course I would usually have an adopted textbook that covers most, then I would need to pull some material from somewhere else, but this book eliminates that: it covers what is needed to be a formal "adopted book for a course" but at the same time it has all kinds of neat resources & applications that I can utilize to make the course more interesting + show either applications or dive more into theory.

Thus, I would strongly recommend taking a look at this book for the course you are teaching, & if you are a student I would recommend looking at Simmions' books to study from, his ODE book is very readable + covers a lot of material & his topology book is a classic in the subject but can be read with some patients + a good understanding of introductory real analysis..