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

I am currently working through this book. Other reviewers have mentioned all the good points and features of this text. However, given the text is 920 pages long, the reader would normally be required to invest a lot of time working with it. With that in mind, it is natural to ask the all important question: whether this book is really for you? My answer is that it depends on your mathematical backgrounds.As we know, Kline's approach to this book is intuitive. Kline argued that "intuition" is the way human's mind learns things; and he is right on. Especially with calculus whose essence being a collection of "mathematical methods" fundamental to the understanding of physical world. To study these mathematical methods without understanding or appreciating the physical problems or applications which gave birth to their (the methods') development is therefore meaningless and shallow. On this point alone, Kline's approach is a first rate introduction to calculus. On the other hand, Kline's text despite being quite thick never progresses beyond these intuitive functions; instead Kline spends a lot of space discussing elementary topics like analytic geometry and application in economics or examples from Newton' Principia. Very interesting of course, but one cannot find a rigorous discussion of functions or imaginary number or convergence of infinite series, all of which are essential basics for those who would progress to higher courses in analysis. An important question that it raises is: to whom this text is actually for?My answer is that Kline's text works best for either those whose high-school math backgrounds is in a pretty bad shape but want to know calculus or for those who have learned calculus a long time ago and are now in a "serious need" for some brush-up. Also for certain high school students who like physics but have never been at home with math, this book is really the missing keystone. There are many other good texts out there like Spivak's or Apostol's or Hardy's Pure Mathematics. These are ideal for college students whose high-school math is still fresh and strong and thus are more able to appreciate deeper/advanced topics like the foundation of number system or analytical treatment of functions. For these students (especially pure-math B.S. students), calculus texts that gear toward analysis (i.e. more rigorous) would better prepare them for future challenges. However, for people like myself, whose math education ended 14 year-ago in high school and who barely remember the cosine rule, working through texts like Spivak's or Hardy's simply lead to a bogged down. It should be remembered that Kline's calculus, first written in 1960s, was introduced during the time when most students were not exposed to calculus in high school. Thus, it was quite a problem when they had to encounter calculus for the first time in college. Back then it would be quite a blunder to demand that kids have to learn both techniques and rigorous foundations of calculus, the first truly "higher math" they ever encountered, at the same time. I think Kline's text was written especially to remedy that problem. However, as most kids of our time are all exposed to fair amount of "intuitive" calculus in their school years, it may not make much sense to require to learn intuitively again in college. Still, I would maintain that even good students would profit much from at least taking a look at Morris Kline's text, for it develops the subject in a strong historical context and is quite broad in the materials covered.All things discussed, this book is a truly 5-star treatment of calculus. Given the state of education and teaching in our times, no one might ever write like this again.[Note: PDF file of solution manual (about 260 pages) can be conveniently obtained by writing to Dover Publication. Great job! Dover, for making this book available and affordable at the same time.]

***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.