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

I am currently a high school senior taking Calculus BC (which is essentially Calculus I) and this book supplements creative and fun applications of calculus that I sometimes am deprived from in class due to limited time. The best parts of this book, other than applications, is how Kline does not quickly rush into an equation, theorem, etc. He explains the notation, what the variables represent as a whole, rearrangement of the equations, and what they can be applied to. Then he proceeds to work through the problem. That, in my opinion, is the most refreshing part of this book and makes it worth purchase.

Great book to get if you trying to learn Calculus from a different perspective. I am an engineering major at the University of New mexico. When I took Calculus for the first time I had difficulty in trying to understand the basic idea. I read through the first few chapter of Kline's book and the readings helped me grasp a good idea of how to understand the idea of differential Calculus, meaning the explanation and significance of the derivative. It's a little difficult to put into words the help this particular book offers because not only does it assist in explaining the threshold of advanced mathematics but it also provides examples of areas of study the material can be used in, but I'd say the examples might prove to be much more useful among bio-medical or chemical engineers.

Morris Kline takes the reader on a journey through calculus with this book. The explanations are clear and easy to follow if the book is read carefully. Kline shows the reader many derivations and explains concepts in wordy paragraphs. Some people may not like this, but I believe it makes the book easier to follow. I recommend this to any future scientist, engineer, or technician who wants an intuitive understanding of these powerful tools

Just like a recent reviewer, I am not happy about this book. It is far too wordy for its own good. And I find it very annoying that all examples use UK Imperial measures. Often the metric equivalent is provided as well, but typically not for the constants. The author does not even know the metric system. He claims that the unit of measure is centimetre and not metre.

As a high school teacher of mathematics and one who truly loves the subject, this is one of the better introductions to the Calculus (others include "Calculus Made Easy" by Silvanus Thompson and "Calculus: A Liberal Art" by W. M. Priestley). Kline, one of those rare teachers who can really communicate the subject, is at home in explaining the "hows and whys" of this most fascinating and beautiful mathematical tool and he even includes review for those still weak in some aspects of algebra and coordinate geometry. Some of the reviewers of this book have complained about the lack of a solutions manual. It is available. Contact Dover Publications ([...]) and they will send you a PDF version free of charge! Because of the availability of these solutions, this book will serve as an excellent and inexpensive source of study (for upper level high school, first year college, independent study, or as calculus refresher) for mathophiles for many years to come.

This is an excellent test for learning calculus for those interested in more practical knowledge about math. The more hardcore mathematician will shun this book on the basis that it does not teach math as the abstract subject that pure mathematics really is.

However if you're a science major other than pure mathematics this book will be indispensable. Even if you're a math major all you must do is keep in mind that it is the abstract concept of each technique that you must derive from the application given. But this is the exact reason why most readers will find this book valuable, because it teaches the math by application rather than abstractly!

This book will most useful for the physicist, engineer, chemist, or biologist to be. Of course this is because most of the applications are given in physical terms (as you can tell by the title).

Also the content of the book is quite extensive. This book should cover nearly everything in your basic calculus sequence. Once in a while Mr. Kline will use "proper" math terms such as abscissa instead of "x-coordinate" which takes some getting used to. But like any science it's good to learn the different terms and jargon. To help with when I forget these while in a different chapter I picked up Barron's Dictionary of Mathematics Terms ISBN# 978-0-7641-4139-3

This book is pretty thick though, which makes it difficult to carry in a bag already over packed with your class required text books. But if you use it to learn the concepts themselves or as an auxiliary to your textbook you won't be disappointed.

I wish this book was available in Kindle, PDF, or E-pub (basically any ebook format). I've contacted Dover books about this, but they said at the moment they don't plan on making it into an electronic publication. Perhaps if more people will request it in kindle format above.

But back to the book. Get it, you won't be dissappointed in the material within. In addition for I also highly recommend The Calculus Lifesaver by Adrian Banner ISBN#978-0-691-13153-5 and How to Ace Calculus by Adams, Hass, and Thompson ISBN#978-0-7167-3160-3 With these you should be able to quickly and easily learn anything for the basic Calculus sequence.

Thanks and good luck in your math adventures. :D

I've taken math through Calc through high school and college. No book has done a better job of explaining how it works than this one. All math books should be written like this one. Clear and practical. If there's something you need to know, he tells you exactly what it is. Such as, if you need to know something from trigonometry, he explains it well enough that you will either understand it or know what to look up in another book.
However, do not think this book needs other books in order to get through it. You should have already had trig and algebra and geometry. But even if you've forgotten it all, this book will get you through to the end.

This book has to be the most transparent and accessible maths book I've ever read - and I've worked my way through a few! You sense that the author understands the subject and doesn't' fudge any of the details. That's why you can't fail to understand what he is saying to you. I never knew calculus could be so easy and stimulating! Along the way you learn a lot about the physical world. This guy writes with a patience and clarity that you normally only find in English literature. Every page is a journey!

If you are interested in doing all the exercises and want to check all your answers you can get the answers sent to you in a pdf format by simply contacting :

[...]
they are super-fast at responding too!

This has to be the only calculus book that you would ever need.

Read it and grow!

(ps, his 'Mathematics and the Physical World' is also a fantastic read!)

Boyce Franks
Scotland

This book doesn't have all those eye catching color visuals, but what makes this book great is its content and way of explaining concepts of calculus. There's a lot of reading which might seem cumbersome at first glance, but ultimately it's worth every second spent on reading. In many calculus book I've seen, there's a theorem, proof of theorem sometime, few examples and then exercise. This book more emphasizes more on discussing theorems and different concepts, proofs of theorems and why, how they work. The book is not very rich in examples, but once you get the concept, you'll be able to do any example. Also the examples that are given, explained thoroughly. So except for the quantity of examples, I have nothing else to complain. Thanks to Doverpublications for making such book affordable ...

This is by far my favorite calculus text. The selection out there ranges from cookbook (Stewart and Anton), to elementary (Adams), to quite advanced (Apostol and Spivak). This book really doesn't fall into any of those categories. Proofs are based on heuristic arguments rather than strict adherence to rigor, but this doesn't mean that the book is "dumbed down." Most people go through proofs in Apostol and wonder what they just read, whereas those in Kline greatly enhance the reader's ability to learn the material. Kline may sacrifice rigorous formalism for increased understanding, but most students of calculus will consider this a very good trade off. If you are looking for a theorem-proof, theorem-proof, ad infinitum treatment of calculus, this is probably not your book. If you are looking for a way to really learn the subject from a very gifted teacher, developing your mathematical and physical intuition in the process, then Kline is the best text you can get.

I fully endorse Patrick M. Thompson's review. As a former humanist approaching the sciences, I consider the perspective of something now being under development: popularly, though somewhat imprecisely, dubbed interdisciplinarity. For someone, I am thinking particularly of humanists, who wants to approach science, the book by that great openminded person, Morris Kline, is exceptionally focused on understanding in addition to the more prosaic solution-finding. His book and Mansfiels-O'Sullivan's Understanding physics, might be evaluated together, almost as a packet for the "someones" I just referred to. The two books dovetail beautifully, the M.-O'S. book also presenting a most readable, helpful and very well-written account. As one who is,indeed, "over 13" (76, with 30 years at the Norwegian Inst. of Technology), I am familiar with most of the problems involved in serious intedisiplinary engagement. Both books together represent

a source of stimulation and show you it is possible to break through the conventional academic barriers without feeing lost - exactly what is needed today.

Note 1. for Amazaon:it may interest you to learn that the M.-O'S book when shipped, would cost more than I pay for it at the Techn. Inst. bookshop (exactly 500 NOK).

Note 2. What do I do when a book I have paid for and which I need, never arrives. I don't care must about measly 20 USD, more abut having the book (Foundations and fundamental concepts of mathematics, purchased 21 August 2005). With best wishes. Staale.

I totally agree with Kline in that calculus, at the beginning anyway, should be taught in an intuitive way, since 1st-years aren't used to mathematical rigor. There is plenty of time to get used to the more abstract, rigourous approach to doing calculus/analysis. This is definitely one of my favourite intro calculus books.

This book is replete with annoyances which constantly impede my progress. Kline's informal language works well for initial calculus concepts, but begins to break down as the subject expands to more complex problems. The examples he gives sometimes end up being completely irrelevant to the concept he's attempting to teach, and His somewhat anachronistic notation and insistence on imperial units don't make things any easier. I'm using this book in a calculus based physics and chem course, and constantly translating formulas into feet and gallons just to get my homework done is a nightmare; (even though I'm American I still like to think and work in metric). As another reviewer mentioned, most of his explanations rely on intuitive guessing rather than complete proofs. While it may be intended to provide an intuitive lesson on each subject, the effect comes off as condescending at best and confusing at worst. Lastly, the solution manual is a joke: his answers are mostly incomplete and sometimes simply reiterate the problem without providing any further guidance. Any hope of reverse engineering a complex integration technique or tricky formula quickly disappears. Individually, all of these problems might be small concerns, but combined they render the book nearly impenetrable and overly frustrating.

A textbook should include everything a student should realistically require to learn a particular subject. Leave it to a flesh and blood teacher to decide what to include in the education of his students. If it wasn't for my excellent teacher I would be completely stuck. As it is, I'm slowly fighting through this tedious jungle of a book with seemingly no light at the end. After a particularly frustrated weekend resisting the urge to tear this book in half, I decided to write this review in order to calm myself. I'm feeling much better now, but I pity anyone who has to struggle with this book like I did. If your teacher assigns this book for your class, try to talk them out of it.

I cannot recommend this book to anyone in good conscience. Its style is way too old, too slow, too painful to read. I couldn't finish the book. It goes through many minute details that you don't need to know about at all. I will be selling it back at the earliest chance I get.

This book represnets one of the best resources on applyed calculus, and also ti is one of the greatest university level introductory texts, much more recommended for scientists than for engeneers, Morris Kline presents an INTUITUVE approach to calculus ideas, based on the PHYSICAL motivation of this area of maths.

When it comes to explaining the basic theory and techniques of the calculus this book is essentially no better and no more intuitive than the usual low-level introductory books; it comes with the usual quasi-pedagogical idiocies, such as guessing limits from numerical calculations and so on. The word "intuitive" in the subtitle is misleading (at least to me, "not formal" does not imply "intuitive") but the word "physical" is more justified. There are indeed quite a few interesting physical applications.

One interesting application, known already to Newton, is this: dig a straight, friction-less tunnel from New to Paris; then if you jump down the hole in New York you will arrive in Paris about 43 minutes later.

Another interesting application is projectile motion with air resistance. Assuming that air resistance is proportional to velocity, F=-Kx', we find that F=ma reads x''=-kx' for the horizontal component and y''=-g-ky' for the vertical component (k=K/m). With initial firing velocity v and angle A the solutions are x=((v cos A)/k)(1-e^(-kt)) and y=-gt/k+((v sin A)/k+g/k^2)(1-e^(-kt)). These formulae allow us to make some qualitative comparisons with ordinary parabolic motion. Also, an interesting special case is pure vertical motion where we have my''=mg-Ky' so y'=-(mg/K)(1-e^(-Kt/m)) and so the limit velocity of a freely falling body is -mg/K.

Another application is pendulum motion. We wish to find s(t), the elevation of the pendulum measured along its arc. The force involved is the component of gravity that pulls in the direction of the tangent; this is -gm(sin A), where A is the swing angle, so F=ma says ms''=-gm(sin A). But sin A=opp./hyp.=(horizontal displacement)/(length of pendulum L). Now here's the trick: horizontal displacement is kind of equal to displacement along the arc, i.e. s(t), at least for small A, so we get s''=-(gm/L)s, so a solution is s(t)=C*sin(sqrt(gm/L)t).

Another application is escape velocity. The quantity (mv^2)/2-G(Mm/d) is seen to be constant ("conservation of energy") by differentiation, and if we have just enough initial velocity to escape to d=infinity we will get there with zero velocity v=0; plugging in these conditions we see that the constant is zero, so we can solve for initial velocity, which will be sqrt(2GM/R).

I used this book to introduce myself to calc, and it teaches/explains concepts very well. I would highly recommend buying this book as a fundamental text for anyone want to learn calculus. It is quite long, so commitment is a must. I bought a used book at very good condition, but the cover/spine was more worn out than advertised. However, the pages in it were in pristine condition. If you intend to completely commit yourself to learning calculus, I recommend buying a completely new book if that's something you can spend the extra bucks for.

This book should be used in conjunction to a textbook on calculus. It helps to clarify some formulas that are not explained well in the standard texts.
It contains a fair amount of useful information for a small size book and the price is fair
It is entertaining to read this book and it gradually become a favorite book on your shelf