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Calculus, One-Variable Calculus with an Introduction to Linear Algebra: One-variable Calculus, with an Introduction to Linear Algebra v. 1Hardcover– 6 Jun 1967

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First Sentence
The remarkable progress that has been made in science and technology during the last century is due in large part to the development of mathematics. Read the first page

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 famous two-volume "Calculus", forming his trilogy of analysis.

Apostol's clarity and precision of exposition are simply unbeatable and his trilogy is to stand high in the collection of anyone interested in mathematics.

To my knowledge, there's only one comparable SUM in analysis, i.e. Edouard Goursat's three-volume "A course in Mathematical Analysis", older (1902), deeper and therefore less easy to absorb, but a definitely lucid and a fundamental classic.

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Most Helpful Customer Reviews on Amazon.com ^{(beta)}

Amazon.com:
40 reviews

85 of 88 people found the following review helpful

Value in Diversity26 Jan. 2000

By
Got'em All
- Published on Amazon.com

Format: Hardcover

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.

65 of 68 people found the following review helpful

The best math book I have ever read21 April 2005

By
matematik
- Published on Amazon.com

Format: Hardcover

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.

Because of its nonstandard approach, I think that this book is unsuitable for most people learning calculus for the first time (especially if you are taking a course and not just studying at your own pace). However, it (along with vol. II) is mandatory reading for anyone who wants to study math, in my opinion.

59 of 62 people found the following review helpful

There is but one Apostol, and he is Tom.11 Aug. 1997

By
Zachary Strider McGregor-Dorsey
- Published on Amazon.com

Format: Hardcover

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.

35 of 35 people found the following review helpful

VERY different from most introductory calculus books--simply amazing!23 Sept. 2006

By
Alexander C. Zorach
- Published on Amazon.com

Format: Hardcover

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.

55 of 62 people found the following review helpful

It's Too Bad !!19 July 2003

By
Jason Schorn
- Published on Amazon.com

Format: Hardcover
Verified Purchase

Frankly, it is too bad that modern academic institutions and those responsible for it's direction have forgone the use of two marvelous and impeccably well-written Calculus texts and in their place have opted to baby students with such authors as Stewart. In the hands of a confident and versed instructor these two texts are worth their weight in gold since they carry the student through the normal Calculus I, II and III sequence as well as providing a nice digression into Linear Algebra. As stated by prior reviewers, these two books are complete, rigorous, Apostol never cuts corners in his presentation of the material and he shows the student exactly how calculus and in general mathematics texts should be written. By far these are best and everything else is merely a waste of paper. My hat goes off to Apostol for continuing to his legacy of well-written Mathematical texts