Calculus and Analytic Geometry

The second half of Thomas-Finney is devoted mainly to three-dimensional analytic geometry, multivariate calculus, and finally vector calculus. Partial derivitives, conic sections, vector-valued functions, and multiple integrals are just some of the topics covered in the second half. Here too, the book devotes ample time to examples and applications. The presentation of advanced concepts is top-notch.

The text is also interspersed with mathematical biography and sidebars that explain how to use CAS to help understand concepts. These are well presented and do not take away from the core math taught in the book.

I taught myself calculus during a summer using this book and without teacher intervention. It was the only one of five calculus textbooks that presented material clearly and simply enough to understand without outside help. In my mind, that's the highest compliment a math textbook can be given.


This is the best   October 1, 2004
O'Young (Georgia, USA)
17 out of 20 found this review helpful

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.


A manditory read for Science Majors   October 8, 2003
K. D Rogers (Detroit)
14 out of 17 found this review helpful

Use this book along with CDs on intermediate algebra Calc I and Calc II from www.thinkwell.com. as an excellent way to start your college studies.

I especially liked the depth he went into with conic sections. I for one had not had that much prior use for conic sections. Newton did. He invented calculus in order to answer specific questions and that involved conics. I like that the writer goes beyond using some of Newtons conclusions and goes into more depth. If you dont like depth, then you can read the first first half of the book and stop there (as is done by most nonscience majors). I have seen other calculus books and specifically bought this once because I dont like just memorizing formulas. I wanted to know more about why this subject was invented in the first place.

The amaising thing is that if you get through this book, you will be able to understand some math and physics known a few generations ago only to Newton and Libenez. Dont you feel smarter already? Even if you have read other calculus books, read this one!


Excellent book (5th ed), I still own it and use it ...   August 11, 2009
Donald Gillies (San Diego, CA United States)
5 out of 5 found this review helpful

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.