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Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra [Hardcover]

by Tom M. Apostol
4.7 out of 5 stars  See all reviews (36 customer reviews)

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Book Description

January 16, 1991 0471000051 978-0471000051 2nd
Volume I presents one-variable calculus with an introduction to linear algebra and volume II presents multi-variable calculus and linear algebra, with applications to differential equations and probability
Title: Calculus.
Author: Apostol, Tom M.
Publisher: John Wiley & Sons Inc
Publication Date: 1967/06/20
Number of Pages:
Binding Type: HARDCOVER
Library of Congress: 61011601

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Editorial Reviews

From the Publisher

An introduction to the calculus, with an excellent balance between theory and technique. Integration is treated before differentiation--this is a departure from most modern texts, but it is historically correct, and it is the best way to establish the true connection between the integral and the derivative. Proofs of all the important theorems are given, generally preceded by geometric or intuitive discussion. This Second Edition introduces the mean-value theorems and their applications earlier in the text, incorporates a treatment of linear algebra, and contains many new and easier exercises. As in the first edition, an interesting historical introduction precedes each important new concept.

Product Details

  • Hardcover: 666 pages
  • Publisher: Wiley; 2nd edition (January 16, 1991)
  • Language: English
  • ISBN-10: 0471000051
  • ISBN-13: 978-0471000051
  • Product Dimensions: 10.2 x 7 x 1.2 inches
  • Shipping Weight: 2.6 pounds (View shipping rates and policies)
  • Average Customer Review: 4.7 out of 5 stars  See all reviews (36 customer reviews)
  • Amazon Best Sellers Rank: #344,336 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews
73 of 74 people found the following review helpful
5.0 out of 5 stars Value in Diversity January 26, 2000
Apostol's presentation differs from the standard order and content for a calculus course, but is the more useful for it. Introducing integration first is historically more accurate and sets the tone for the rest of the book. This is not a "plumbers" book but the examples inform the abstraction very well. This book does not bog down in the tedium of analytical geometry and figure recognition which is too often the case elsewhere.
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.
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56 of 58 people found the following review helpful
5.0 out of 5 stars The best math book I have ever read April 21, 2005
This book is extremely well-written and leaves you with the feeling that it couldn't have been better. A tribute to this fact is that it is still in its second edition from 66 and, though it is rather old, has kept its quality.

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.
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52 of 54 people found the following review helpful
5.0 out of 5 stars There is but one Apostol, and he is Tom. August 11, 1997
Perhaps the best description for Calculus, by Tom M. Apostol, is simply its title. This text is Calculus. Like no other calculus book I have seen, it devotes itself totally to its subject matter, never compromising itself for the sake of understanding. By doing this, the reader is permitted to learn calculus completely.

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.
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28 of 28 people found the following review helpful
This book, unlike most Calculus books out there, is meant to be read and understood. The way that Calculus is taught nowadays, people use books that are 90% problems, exercises, and examples, with an emphasis on computation. This book is 90% prose, and the emphasis is on cultivating a deep understanding. In addition, the book does away with the gap between "Calculus" and "Analysis", choosing to begin with a more mathematically mature perspective...but providing ample explanation for students who have not seen the material before.

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.
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Most Recent Customer Reviews
5.0 out of 5 stars Rightfully a classic, but criminally priced.
This is a fantastic book and rightfully a classic but a $400+ price tag for both volumes is criminal. Read more
Published 2 months ago by BartholomewHavok
5.0 out of 5 stars If you want to truly understand the topic, look no further
For the scientist in training, Apostol 1 and 2 are must-haves to learning calculus.

I had the privilege of learning Calculus from the author himself at Caltech, using... Read more
Published 9 months ago by Picky Buyer
5.0 out of 5 stars Apostol's superb trilogy of analysis
The two volumes of Apostol's "Calculus" must be linked to his "Mathematical Analysis".

I consider "Mathematical Analysis" as the third volume, complement to Apostol's... Read more
Published 15 months ago by André Gargoura
5.0 out of 5 stars The Best
The Best. Period. I have to write 20 more words but there is nothing left to say but Tommy I and Tommy II are the best.
Published on March 29, 2012 by Charles Saunders
5.0 out of 5 stars Wow
Y'all been holding out on me. I feel cheated. Hows come no one ever told me about this book before a few months ago? Awesome book, best Calculus text I've seen.
Published on April 22, 2011 by Kevin C
5.0 out of 5 stars The best calculus book I have read
Perhaps my love of this text is because I was one of those students who only wanted to know how to use a derivative or integral to solve a physical problem when I took my first... Read more
Published on August 27, 2010 by mark
4.0 out of 5 stars A Bona Fide Masterpiece ... With One Reservation.
The name above should read: Old-Time Math HOBBYIST!

Sorry about that! Oh, the vagaries of aging ... to the review of Apostol One:

Oh, the memories! Read more
Published on April 5, 2010 by Old-Time Math Hobbiest
5.0 out of 5 stars Interesting and Very Thorough
I'm not really a lover of math. Mostly I'm a Physics teacher (who uses math). Due to some quirks of the schedule, I've been asked to teach Calculus for the past 2 years. Read more
Published on October 8, 2009 by Jason M. Waskiewicz
5.0 out of 5 stars For the serious mathematician, this book is great
This is a classic calculus textbook. It is more difficult than standard textbooks such as Stewart or Larson mainly because it takes an analysis style. Read more
Published on September 9, 2009 by jacksarewild
5.0 out of 5 stars Ad astra per aspera
As a former student of Tom Apostol, I am greatly indebted to his textbooks (both "Calculus" and "Mathematical Analysis") and to his excellent teaching style. Read more
Published on July 13, 2009 by V. N. Dvornychenko
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Topic From this Discussion
Error in proof of theorem 4.3?
The difference quotient Q(x) is continuous at x not = c but Tom defines Q(c)=f '(c) and since f '(c) exists, he is filling in that point. Note that by the definition of the derivative, f '(c)=lim(x->c)[{f(x)-f(c)}/{x-c}] , but Q(x)={f(x)-f(c)}/{x-c} and Q(c)=f '(c) , so making 2... Read more
Dec 1, 2012 by Corinne Redding |  See all 3 posts
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