Calculus: An Intuitive and Physical Approach (Second Edition)

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.

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.

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.

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.

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.