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

The good thing about texts relating to mathematics is that it is hard for them to become out of date. This book was published in the 1960s, but I find it to be perfectly able at teaching the calculus. In one of my classes, I even saw another fellow with this very same book.A full solution manual may be easily obtained by emailing Dover Publications.

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.]

I felt obligated to write this review, because as a good but rusty math student, I would like to help others find the right book according their own needs.First, back in my day, I studied 4 semesters of Calculus in college and considered myself to be good at math at the time - but that was 30 years ago. After my high school daughter came to me asking for help with deriving functions, I was in search of a primer that would be more comprehensible to me than her school text book. I ordered this book and was sadly disappointed at first. It is long, with small print and almost philosophical about math. I found it to be no better than her class text book when it came to reminding me of the rules for deriving functions like the product, quotient and chain rule. I ended up ordering a book with the word "dummies" in the name though I won't say exactly which one and that suited my purpose immediately. In 30 minutes it all came back to me and I was able to sit and help her understand the basic concepts at a high school level and work through homework problems.Now back to this book - the next day I picked up this book again and began reading it without the pressure of needing a quick, to the point answer or lesson. I began to read it, not as a text book, but more like an academic novel about math and that is when things started to click. It gave me a new appreciation for why calculus is important, how the derivative is not just the slope of the tangent, but the direction of a line at any given moment and why that is important to motion, targeting moving objects (military applications) and light striking lenses (optics). Ah, that is very cool stuff to wrap ones head around after many years of work that required little more than a 5th grade education in my corporate IT job!Given my new appreciation of this book, I will be reading more as I hope to understand concepts and drivers behind more advanced math concepts - both as a reminder of what I forgot and for new enlightenment. I don't expect to use this book to advance my own problem solving capabilities - although it may help in that respect too - but rather to gain a more enlightened appreciation for Calculus. The book includes exercises and problems along the way as well as answers for about half of them - an excellent complement to help one confirm they're grasping the material.In summary, I would not recommend this book if you're new to Calculus or trying to get through a high school or college level course - but if you're a advanced math major or even an old guy who wants to get a better appreciation - almost an academic, theoretical or philosophical appreciation - for advanced mathematics then this is the book for you. Just don't use it as a primer to help your impatient high schoolers and who need quick answers and bulleted minimalism.