Calculus: An Intuitive and Physical Approach (Second Edition) (Dover Books on Mathematics)

I first took calculus over 20 years ago and always did well in math, so I wanted a text that I could keep as a refresher (for studying more advanced statistics) and reference for things I may have forgotten. So my experience with the book may differ from someone who has never been exposed to calculus before. In my opinion, this book is an excellent introductory text for single variable calculus. While it is a bit dated (it's a reprint from 1977), given its low cost, compactness, and how comprehensive it is, I think its value is unbeatable (especially compared to current university calculus texts).While there *are* some drawbacks/negative aspects, I think they're pretty minor but they should be pointed out either way:1) Typos -- there are a non-insignificant number of typos throughout. Some of these are trivial to spot, while a few were in the answers to select exercises. I spent time scratching my head trying to match the printed answer when it turns out there was a typo. This might be a bigger concern for absolute beginners.2) Graphics -- the figures are clearly very dated and don't have captions. However, this isn't really a problem until the later chapters on functions of more than one variable, and even then I thought they were clear enough.3) Content -- I found the book a bit verbose in some places, but this may be more appreciated by a beginner. Also, if you will never take introductory physics, you might struggle with or be frustrated by how many of the examples and exercises are specific to physics problems (even though this is, historically, how calculus came about).4) References -- since the book is so long, it would have been nice if the author included page numbers when referring back to a particular chapter/section/equation. He sometimes does this, but it isn't a big issue.Overall, I don't think anyone who will need to use calculus would be disappointed in having this book around. There are chapters and sections marked as optional, a comprehensive list of integrals of different forms at the back, and the author explains concepts intuitively. For the most important theorems and ideas, I use post-it tabs for quick reference.

***On the BookI already have taken basic calculus courses not that long ago, so I used this book more for reviewing and "honing" purposes, and I couldn't be more pleased with it. The author details many derivations that were skipped in my calculus courses, for example the derivatives and integrals of inverse trig functions, the formulas of which us clueless students were forced to memorize. After reading this book, never again would I have to futilely batter my brain cells in the frantic search for a formula I was not able to retain - this is the best quality about the book. Ordinarily, students would be taught math (or any other subject) in a way that would induce them to score well on tests. This technique is shallow and often cuts corners, as some steps are left out for fear that it may confuse the test-taker, who inevitably takes his test unthinkingly.Kline's [the author] teaching philosophy is different. He sets out everything in detail and with clarity, so that the student may himself solve problems without resorting to formulas or hoping that test problems would not differ from the drills he has solved. Furthermore, the practice problems in this book are engaging, and Kline has take great pains to show how every mathematical technique can be used in real life. Some of his practice problems also asks that the student prove some thing or other (it is not all application), and this allows the principle to further sink in the brain.A solutions manual is not included in the book, but may be requested, for free, from Dover. The details of how to do this is described in one of the front pages where the copyright information is found. The solutions manual could also be found in Dover's website. It is in pdf form and is something like 250 pages.The solutions in the solution's manual do not merely list the correct answers. It also describes how to get to that answer. There are some typos, so there may be moments when no answer of yours would be correct now matter how and how many times you get at it. I do not believe the typos are anything major, since it can be obvious when something is a typo. Besides these atypical moments, the solutions manual could be regarded as having the infallibility of God, and with inducing the same soul-enriching effects.Some people may complain about the wordiness of this book, but the "wordiness," in my opinion, aids in the understanding: it is a blow-by-blow description of the proofs and model problems. It could be skipped; I mostly don't.I highly recommend this book.***On Amazon:I have already bought a book from Amazon before, purportedly new, but when I received it, its spine was wrinkled, a fabrication error I suppose. It was also evident from a number of other minor damages that Amazon does not take good care of the books in its store. The book was far worse-looking than many of the used books I bought from outside sellers. Now, I bought another book from Amazon, this one, and it was no surprise that it was worn-looking and evidently manhandled by whoever was in charge of Amazon storage. I was willing to overlook that, what I can't abide by is the stains I found on pages 347-351, and goodness knows how many more stains and surprises lie in wait. Is Amazon trying to pass off used books as new? I am sick of how Amazon handles its products.