Customer Reviews

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

5 star:		(27)
4 star:		(4)
3 star:		(2)
2 star:		(1)
1 star:		(0)

 

 

Morris Kline has written a really excellent book here. It is somewhat different from the typical calculus books one reads: there is less formalism and greater apeal to your intuition (hence the title). Kline works hard to ground the book to reality, so is it useful and applicable, rather than just an exercise in superficial algebraic regurgitation as so many others teach calculus to be. This is a work that wants you to understand not only how...but why! This is a truly important approach: because if you understand why, then you understand how and you have the flexibility to really use the calculus. Just knowing how means you loose some of the connection and treat it as a process rather than a tool. This books at times feels deep, like the philosophy of calculus in addition to a howto, not just a perfunctry, dry how-to.

Kline provides realistic examples and focus attention on scientific and practical uses of calculus: eg motion down a inclined plain, projectiles, etc. There are lots of problems in each section. ONly complaint: the answers are a little sparse at times. Generally the problems are robust and a little tricky know and then (this is good! Makes you interpret and apply...not just apply). The literacy components are quite strong in questions. Kline has an excellent teaching pedagogy!

The style of writing is excellent, familiar and warm. Kline write like he is like that smart, cool, friendly lecturer we found once at university and longed for the rest of the time we were there. He clearly loves what he is teaching and wants you to succeed and tries to help you to do so. His language is not so stilted as most mathematics books seem to be; humor creeps in here and there which is cool because it makes you feel welcome inside the book, not just a nobody to whom the author is indifferent.

The book is arranged in a typical sequence (you can look inside the book and see that). And is the best value for money calculus book I have EVER seen: it is VERY good. 960 pages of quality. If you want a book of calculus problems buy Schaum's...but if you want to understand calculus...buy this! of course this an introductory calculus book so there is no vector calculus, but it does get multivariate!

In all: well worth the 5 stars and the cool price! SHame more books are not like this one.

Note: if you write to the publisher (Dover Publications, on the web), they will kindly email you a copy of a PDF file containing the full text of the answer key. I was grateful because without it I would be lost!

I'm only on page fifty or so of the book, and it is very good so far. It's rather challenging (read: hard). However, considering that it is actually making you apply what you're learning to actual concerns of real life, the sweat on the brow is a good thing. (I'm just doing this for fun--it's been 14 years since I've had a math class, so hard for me might be easy for the young laddies and lassies coming straight out of trig.)

If you've had physics, you probably remember having had to memorize lots of kinematic equations. In this book, Kline actually walks you through the process of _making_ the equations by using Calculus--pretty nifty, and something that is lacking in most high schools: math and physics hand in hand.

UPDATE - SOLUTIONS MANUAL
=========================
A number of people have contacted me trying to obtain the Solutions Manual to this book. I've posted a copy on my website because it is freely distributable to users of the textbook. However, Google web search has not picked it up for some reason. However, if you go to Google Books, in my review of the Solutions Manual, you will find a link to my website so you can download it. In Google Books, search on the ISBN of the Solutions Manual, ISBN-10: 0471023965 or ISBN-13: 9780471023968, in order to find it.

You can download it here, if Amazon lets the URL stand in this review: [...]

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 (www.doverpublications.com) 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.

I wish I could give this book 10 stars. I made a "D" in my college Calculus class. It wasn't that I didn't understand how to do problems or didn't try, it was that I didn't know WHEN to apply what I knew to certain problem sets. This is your answer. Kline explains in detail (without getting too deep) WHY, WHY we use limits, WHY we differentiate, answers my Peruvian Calculus teacher never answered. I can't even begin to tell you how excellent this book is! The problem sets are intuitive, based in reality, and are applicable to me! After doing problems in this book and making it to where we left off in Calc I, I bought my old Calc book that we used in class. No wonder! I wish that more textbook authors took the time and made the effort to make sure that their materials is as clear and concise as Kline has. His explanations are obvious, he doesn't skip steps, and he works with simple numbers (base 10s) so that you understand WHY and HOW. His problems get progressively more difficult, which is awesome, because it gives you the confidence that you know what you are doing once you have finished the problem. If you have a hard time with Calculus or you just want something to do, BUY THIS BOOK. It is an excellent resource and an excellent textbook.

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.

Kline does a superb job at covering a wide range of topics in calculus, while presenting them in a clear and relatively in-depth manner. This book is not only great for someone who has no experience in calculus, but it also great for someone who is reviewing the basics. Although the size of the book is somewhat intimidating (950ish pages), the book is written in a very readable and logical order. Also, interspersed throughout are some extra sections that discuss specific physical applications of the techniques studied in that chapter. Personally, these sections are fascinating and quite rewarding. It succeeds both as an overview/introduction to calculus and as a segue to higher mathematics. If you are just starting out on your voyage through calculus or are brushing up on the basics, this is the book for you.
One small problem is that there are only answers listed for some of the questions in the problem sets. These answers are listed right next to the problems themselves, so they are difficult to cover up. Furthermore, the solutions manual is very hard to find, if it is available at all. My advice is to do the problems from a different text that has answers and just read straight through this book. Other than that, however, this is a great book.

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.

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.]

This book provides an excellent introduction to Calculus. I've looked at many instructional books and this is by far the most approachable and the easiest to understand.

One of the drawbacks given for this book is the lack of solutions for the study problems but this problem has it's own solution in the form of solution guide available from the publisher for free.

If you have the time, patience, and the inclination to get a strong introduction to Calculus then this book will probably meet your needs. Note I say 'probably' because for many of the young folks today the text may seem wordy and overly pedantic. Kline forfeits the graphical techniques of learning for the verbal. So one has to carefully follow the explanations. Later in the book graphical explanations for things like differentiation are explained.

So if you expect a fast paced text like say 'Calculus for Dummies', 'How to Ace Calculus' etc you will be disappointed. What I found helps is to get going with some modern quickie texts like Dummies etc and then go with Kline's work. This helps firm up some theory instead of just learning the mechanical stuff. Also, as others have pointed out, but this needs to be mentioned, the answers to problems can be obtained via a PDF from Dover. They answered my email promptly.

If you want a good reference for introductory Calculus without say the rigor of Apostol's text this is a great investment that should serve you for years to come. Excellent textbook.