Calculus: A Rigorous First Course (Aurora: Dover Modern Math Originals)

I owe so much to this book. I had not done any math in 9 years but I felt an urge to pick up math again, which was my favorite thing to do in High School. This book is clear concise. It has made me so confident in my mathematical abilities. I just want to thank professor Velleman. I have gone on to purchase his other book, "how to prove it". He makes you understand limits, write proofs, understand the derivative, the integral and more. His writing has a lot of personality as well. This is a serious math book but he finds clever ways to inject humor as well. I have completed this book from cover to cover. It took me 8 months. I spent a lot of time on the exercise to get a solid grasp of the concepts. As you progress in the book, your familiarity with the concepts increase, you begin to grasp things without rereading as many do for several math books. I just owe my now very keen interest in mathematics to this book

This is the VERY BEST calculus text I have encountered. I am by no means good at math but I have trudged through quite a few calculus textbooks in my time culminating with Apostol's classic. But here Velleman has a unique presentation model that gets into the minutiae step by step. I got this book for Christmas in 2020 and I am now just starting chapter five. I am struggling but enjoying every moment. Most sections I have to go over at least three times to digest the stuff. Now that I am retired gone are the days when I got through exams and tests using standard college level calculus textbooks. This time I'm taking it slow. This one is a gem of the first order.

Hasta ahora solo lo he leído superficialmente, pero me parece un buen libro para iniciarse en el cálculo. El libro llegó con un pequeño golpe en la parte de abajo del lomo, pero nada grave. Por lo demás, muy buen servicio.

Book arrived on time and in great condition!

The way calculus should be presented. Pencil and paper, no technology. But, if you know how to use a graphing calculator this is a very inexpensive way to learn calculus. If I were a professor, I would use this (or Lang's) text with supplemental tech material.

Perfecto para aprender cálculo de la forma correcta.

Enthusiastic 5 stars for this work. Disclosure: I'm neither a mathematician nor a student of mathematics in the traditional sense; rather, a chap who uses mathematics in his profession, as well as a "math hobbyist" of sorts. It's in that latter context that I've read or at least skimmed many of the well- and less-well-known calculus texts: Apostol, Stewart, Thomas, Spivak, Morris Kline, Adrian Banner, Stanley Grossman, and a boatload of others. Against that background I give Prof Velleman's text an energetic recommendation for anyone seeking a deeper understanding of single-variable calc concepts than what one normally encounters at the elementary level. I was already an enthusiast of Prof Velleman's "How To Prove It" before encountering his Calculus text. Having read (no, absorbed) Prove It, I knew what to expect with his Calculus, and he didn't disappoint. More than any other calculus-text author I've encountered, Prof Velleman's approach guides the reader in developing a way of thinking characterized by a careful dissection of a problem to fully understand the picture, followed by a very careful, logical, step-by-step thought process to arrive at the solution. Mr Velleman's strong suit is in explaining this thought process in a consistent manner, from the first page to the last, such that the dedicated reader can't help but acquire this manner of thinking over the course of the text. As one case in point, Prof Velleman's exposition of limits of composite functions is hands-down the most illuminating I've encountered. For another, his novel notation of adding an inequality symbol as a superscript in the "x approaches the point c" portion of a limit statement, repeatedly hammers home the reminder that the manner in which "x approaches c" MUST be kept distinct in the mind from how "f(x) approaches its limit at c". Having read Prof Velleman's calculus text, I often find myself making notes in the margin of other calc texts which begin "see Velleman p. xxx for better exposition...". If Mr Velleman should ever be talked into writing a multi-var sequel to this one, I'll be first in line for a copy. PS: Avoid the Kindle version at all costs, unless you enjoy having the feeling that your brain cells have been dropped into a blender. In Mr Velleman's excellent text, Kindle has rendered many (all? I gave up on the Kindle version after a couple of chapters) of the inequality symbols as equals signs. Completely torpedoed the intended exposition. Example: "Proposition 2.2.1. ... Proof. ... Since |x - 2| > 0, x = 2..."!!! A horrible butchering of the author's point. Also, as I mentioned, Mr Velleman uses an inequality superscript in a certain context to convey a very important idea, in several places throughout the text. I can't think of a better way to discourage a student right out of mathematics altogether than to change all those symbols to equals signs, but Kindle has done exactly that. Do yourself a monster favor and grab the paperback version!

Can be used a a single source for studying calculus

Very conceptual book of calculus.

Only if more Authors could write like this.With crystal clear clarity.Had it not been for the price would have certainly recommended this to students of 11th-12th for clearing out basic concepts and building solid foundation towards solving competitive problems.