Calculus and Analytic Geometry

I used this book for a University Honors Calculus class that I took as a senior in High School. As a math enthusiast (my dad was a Math Professor), and compared to other math books, I would say that the exposition in this book is very very good. The authors were from MIT and U-Illinois, respectively (the latter is where I took the honor calculus class), and at the time it was being used at both schools. Some people have criticized this book as 'repetitive' and 'obvious' but I HEAVILY disagree. Calculus is a set of tools for approaching geometric problems. There are hundreds of tools in this book. My honors calculus professor had us working one sub-section of the book EVERY NIGHT, FOR AN ENTIRE YEAR. In that time, we finished the entire book. I worked 4 problems EVERY NIGHT, FOR AN ENTIRE YEAR. Later on, I attended MIT, and I was helping the freshmen in their calculus homeworks 5 years later FROM MEMORY! Meanwhile, the MIT students, who had less practice (one problem set per week) quickly forgot what they had learned! So I was helping the upperclassmen to remember their calculus, too !! Calculus is the very last "bag of tricks" subject that is taught in most math curriculums. The theory behind integration and differentiation and other techniques are all there, in the Thomas and Finney book. The burden is on the reader to understand the theory, before they jump to the practicum. It's true that Thomas and Finney do not ask you to derive new theorems, but there is too much material to allow this in a 2-semester or 3-semester textbook. I wonder how far people have gone after complaining that there was too much rote practice in this book. In my case, I enjoyed the book and completed a PhD in theoretical computer science.

This textbook is by far one of those actually worth buying. I struggled through that awful, miserable excuse for a calculus text by Edwards and Penney, and was a little more impressed with Stewart and Anton. But I pulled out of my calculus courses and decided to get a bit more preparation in before taking them again. I started out with Calculus Made Easy by Silvanus P. Thompson and Martin Gardner, then went back to by old high school texts and made sure I understood everything. You don't need those huge, expensive Elementary and Intermediate Algebra texts; you can get away with Introductory Mathematics by Petocz, Petocz and Wood, published by Nelson/Thomson Learning (http://www.nelson.com.au). What you need to understand calculus is a good intuitive feel for algebra and to know *why*, not just *how*. There's a big difference. Once you've spent a couple of months sweating over your algebra, geometry and trigonometry texts, it's then time to reap the rewards and learn calculus. Thomas and Finney's Calculus and Analytic Geometry is extremely well written, with the right balance between applied mathematics for scientists and engineers and pure mathematics (proofs and stuff like that). If you're a math major, or intending to become a math major, then you'll want to use this book along with Apostol's Calculus and Spivak's Calculus. One thing I learned the hard way was that putting off mathematics has the effect of slamming the doors in your face. Interesting and useful university courses are out of reach, career options are out of reach, and you're left in the dark when it comes to science and technology. The good news is that with a bit of hard work it will all suddenly fall in place. Mathematics is the foundation of all science and technology, and, of course, the foundation of the exciting new mathematics which will be the basis of technology 30 years from now! Do yourself a favour and pick up Thomas and Finney's Calculus and Analytic Geometry. If you've ever struggled with awful calculus texts, you'll be pleasantly surprised by this one. (Remember, make sure you've got your high school algebra under your thumb).

I recall seeing this book in my living room when I was seven or eight. I'd pull it off the shelf, open to chapter one, look at the word "limit" and feel my mind go blank. Well, six years later, I took AP Calculus AB and I made a five on the test. Many factors went in to that. This is one of them. This book feels very comfortable to read. The margins are very wide and there is a good space between the examples and the text. Professors Finney and Thomas wrote so clearly. Precise and concise. Whenever I didn't understand what was going on in my AP class, this helped to clarify it better. There are ample problems for you to practice and apply what you've learned. It's a shame that this isn't really sold anymore. This is the best. If you can get a copy of this, keep it. So good.

Thomas & Finney, from MIT, set the standard for Calculus texts with this book. It is a book by mathematicians for mathematicians, and is a must-have for anyone seriously devoted to the pursuit of math. As a student, I found it to be very helpful. Though it was not the text used by my class, I referred to it when the text failed or when I wanted to really understand how something worked.