Calculus

Easy explanations and plenty of subject area to cover the first and second courses in Calculus.

I was looking for a little book of calculus I could carry around with me, my textbook from school is just too big. I knew that such a book wouldn't cover every single topic in calculus, but if it covered the major stuff and had good presentation, I would be pleased, since the rest could be filled in using online resources, etc. I saw this book at the bookstore, and thought it looked pretty decent, it was only $13, so I bought it. I'm glad I did, the introduction to e and natural logarithms is the best I've seen. The author is able to explain concepts in the most clear and concise manner, such as is rarely seen. This book is the best little book of calculus I've seen.

Hundreds of Calculus texts claim to teach this rich field of mathematics easily or well. Most texts send students running out of class. As an educator, my goal is to explain all of the fundamental techniques of Calculus, with their proofs, in a manner and pace that a tenth grade inner-city student can comprehend. I believe this is quite feasible using this book as a comprehensive guide if the teacher loves math, uses the text, and loves the students. The self-tests are cogent and progress gradually in complexity - keeping pace with the growing power of the chapters. This is the first book I reach for when a Geometry or Algebra student asks me "Do you think I could ever take Calculus?" You bet! Hugh Neill's masterful "Teach Yourself Calculus". I recommend it without reservation. N. Montero, MD

I used the 3rd edition of Loomis when I took Calculus. The book explains the material so well that I taught myself reading the book. The examples are numerous and particularly good in showing both easy and difficult problems. (Some books only show the easy problems or insufficient variety of them.) If anyone has a trouble with this book, serious review of algebra 2 is recommended. As for some of the previous reviews, there is no section 5.1.1 or 5.1.2, unless they are talking about a previous edition, which I have not seen. There is no mistake in section 5.1 or 5.2. But there are some mistakes in the answers in the back. Looking back at the book now, I prefer what Swokowski did with the series chapter much better (Loomis has interesting discussions on irrational numbers etc, but at the expense of losing the focus.). But Loomis does one of the best job in introducing vectors and functions of several variables. The chapter on Green's theorem is very nice, too. The chapter on multiple integral starts out by stating that it is only an introduction (like any other book at this level). What I realize now is that one has to go on to "advanced calculus" or vector calculus to master those things. I like Shuey's vector calculus, and after mastering that book, Buck's advanced calculus.

I liked the book. It was accesible and unpedantic. I had tried a couple of other sources before this one, and they all had a general tendency to be unapproachable. But it explained things clearly and concisely. It has many examples, and they're almost always clearly worked. The only two things to which I take exception are in section 5.1.2, in which a careless error is made that did in fact leave me saying "what the...", and the lack of creative sort of excercises thoughout the book. To be honest though, I never really did any of the exercises, and I understood calculus very well after reading this book. As one more plus, contrary to most academic books, this one is very cheap. Give it a try!