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Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra 2nd Edition
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Top Customer Reviews
I am using the book for self-study as a middle-aged adult and find the presentation makes sense of things from other sources. The intellectual level is demanding but not unreasonable--challenging without being overwelming. While the introduction of linear algebra may no longer be needed for introductory calculus students, presenting it in the context of the calculus ties thing together nicely.
So many calculus texts in the current market have a sort of misguided focus. Instead of explaining the subject they claim, all they offer is the tools for solving the rote calculus problems of Advanced Placement tests and engineering. This is fine for someone who cares nothing of mathematics, but is not sufficient for their claim of teaching calculus. Apostol's Calculus cares little about explaining the applications of calculus or preparing someone for yet another standardized test. Uncluttered by fancy computer-aided graphics and pages and pages of redundant examples, Apostol offers the basics of calculus with the prrofs behind the theorums. Never once is the reader left with questions as to what exactly integrals are or why any two nonequal numbers must have another number between them. Everything necessary for the reader to solve any single variable calculus problem is presented in text. Apostol's rigor knows no bounds, begining first with the proof of the positive integers and continuing to the finest points of integral calculus.
This text is not for the faint-hearted. If you just want to be able to solve calculus problems, you would have little use for this text. But if you want the tools and justifications for all of calculus, this is the book for you. It is a necessity for all mathmaticians' libraries.
See also Calculus 2 by Tom M. Apostle for multivariable calculus.
This book is exceptional for self-study. I would recommend it to anyone learning calculus on their own, who actually wishes to understand it. This would make an excellent supplement to one of the standard Calculus textbooks, since it addresses just about all the classic weaknesses of these texts. I wish colleges would use this as a textbook, but alas, that would require a drastic restructuring of the curriculum.
This book may come across as "hard" to students, but this is only because it is structured in such a way that one cannot not get through it without understanding the material. Also, a student finishing this book will be ready to dive into more advanced analysis courses, whereas students using basic intro calculus textbooks will find themselves very poorly prepared for these things. The current calculus books with their emphasis on mechanical computation, allow students to get through without understanding the material, and that is why they come across as "clearer". In reality, they are much less clear than this book.
It has a good number of exercises (usually between 15-30 per section/topic), which is less than most standard calculus book, but the difference is that the quality of the exercises here is much higher, and you will be surprised when some months later, when tackling some problem for another course, you will remember having done the exercise in Apostol. It also has answers to all the exercises (except for the ones which require a proof, rather than a number as a result). The problems range from easy to very hard, but usually there won't be more than two problems per section that one won't be able to do upon first reading and a little thinking.
The writing of the book is very good and rigorous, and it covers some topics that are not present in most calculus books. For example it has a small seciton on partial derivatives, it covers the weighted mean-value theorem for integrals and rearrangements of series. There are many other topics that don't usually fit in a calculus course, but the introduction of these when you are still learning it makes the connection between the topics much clearer. After having read the book from cover to cover, it has now become a very useful reference that never leaves my table. Also, because it is rigorous and has a broad number of topics, if you learn this and vol. II now you will save a lot of time later in more advanced courses such as analysis, differential equations, linear algebra and to a lesser extent even differential geometry and probability.Read more ›
Most Recent Customer Reviews
This book deserves a high ranking if for no other reason than to provide answers to all the kids who went through crappy state school education with looming questions about what... Read morePublished 1 month ago by Robert C.
I have studied both applied and some pure math. This book is well worded and very intelligent reference to a mature student in the field, but it falls short of it's own goal as... Read morePublished 8 months ago by Amazon Customer
This book is a classic. It's not calculus for the biology major. If you just want to learn how to do calculations, this book is definitely not for you. Read morePublished 12 months ago by Rick Ferraro
Calculus taught in the perfect balance of thoroughness and practicality. The proofs are aesthetically pleasing, the material is introduced in historical order (read: order of... Read morePublished 13 months ago by Kenneth B
This book is for the serious students of Engineering that want to develop and appreciate fine mathematical development without going into real analysis. Read morePublished 14 months ago by ZEESHAN
My one star rating regards the publisher (Wiley) and not the author (Apostol). First, both volume I and 2 are outrageously expensive. I have the 1967 (Vol. 1) and 1969 (Vol. Read morePublished on August 26, 2014 by David
You could get twelve other analysis books that are of comparable quality. It's a scam for the publisher to charge this type of prize.Published on June 9, 2014 by Nate
It will be a dark day for mankind indeed if these two volumes should ever go out of print. That being said I hope the AMS gets their hands on the publishing rights because these... Read morePublished on February 14, 2014 by Amazon Customer