Salas and Hille's Calculus One and Several Variables

I have two copies, because the first became worn out. Every subject and treatment is well organized and thoughtful. Although I have many mathematics books that offer a more analytic treatment of calculus ideas, for its purpose this is easily the best mathematics book I own. I saw that there is now a looseleaf notebook version available for student, yet I would highly recommend the hardback, as it can be kept for reference into the future. If you only own one calculus book, this should be it.

This is a superb textbook and it's easy to see why the book is in its ninth edition. What I really enjoyed (yes, I know this may sound a little incongruous in relation to calculus) was the step-by-step build-up of knowledge with good, clear examples. Also, for the problems at the end of each section, all the odd problems have solutions, so one can get some practice (something that is unfortunately rare for many textbooks). Before going through this book, I had minimal exposure to calculus and what I had seen wasn't very favorable. This book was a key reason why I now really enjoy the subject and feel very comfortable in this area.

This book is a stunning rebuke to all attempts to dumb down the math curriculum in high schools and colleges. This book, in my opinion, expects the student to have mastered precalculus at the level set forth in, say, David Cohen's Precalculus with unit-circle trigonometry (ISBN 0-534-35275-8). It introduces mathematical rigor in the Calculus 101 semester (of a three semester calculus program) and thereby begins preparing the math major for the hard analysis courses that comes later on. There are no cute stories featuring 'How I Use Math In The Workplace' to inspire you - your self esteem will be hard won as you master the concepts as presented here (especially the problems). The book's greatest strength is that it is basic and traditional in its approach to calculus - no problem or example requires obscure special tricks from mathematical journals or Isaac Newton level ingenuity. This book is a must get!

(This review refers to the eighth edition)This is an excellent textbook for an ordinary 3 semester calculus sequence. Important theorems are not used without proof, the illustrations are simple and tasteful (I hate when math textbooks contain color photographs), and the content is well-written. There's a good balance between theory and applications. This textbook does tend to be more challenging than many undergraduate texts, and may not be appropriate for high school or junior college courses.The least upper bound material would be better placed earlier, before studying integrals. The authors might have expanded the theory involving implicit differentiation and differentials. This is an introductory text, however, and the authors generally make good choices when it comes to including theory. Every university should use this book as the text for their standard calculus sequences.

This is a very good book - I found it really helpful especially because it was quite challenging. If you are a person that does not like math, however, you may want to use a more elementary book first, before doing this one. Has plenty of examples and good problems. Very good for students taking freshman/sophomore college level national exams. Its ideal for university level multi-variable calculus course(s).