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

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 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.

:)

Am a doctor and hence had to leave my love for physics 20years ago. Now that I have settled I wanted to go back to physics. First hindrance came in the form of calculus. So bought a few books on calculus and started working out but couldn’t go past first few pages. Fortunately I could lay my hands on it and instantaneously fell in love with this book. This book is meant to gain knowledge and not for exam preparation. Wonderful book would be an understatement

Fluent and readable introduction to calculus, might seem bit lengthy at times, but always sticking to the point. Easy to skim through the sections that you are already familiar with, and the extra explanation is useful for improvement of understanding of newer sections.

por el precio y la claridad con que expone los conceptos es una gran compra.

Un libro muy completo que enfoca el aprendizaje del cálculo de la manera en que fue concebido, rompe el esquema tradicional de fórmulas y orden en el que se enseñan los diferentes temas en curriculum académico, proporcionando una base mucho más sólida para entender futuros temas en las diferentes aplicaciones de otras materias. Recomendado para nivel bachillerato y licenciatura.