- Hardcover: 666 pages
- Publisher: Wiley; 2nd edition (January 16, 1991)
- Language: English
- ISBN-10: 0471000051
- ISBN-13: 978-0471000051
- Product Dimensions: 6.9 x 1.7 x 10.4 inches
- Shipping Weight: 2.6 pounds (View shipping rates and policies)
- Average Customer Review: 4.4 out of 5 stars See all reviews (48 customer reviews)
- Amazon Best Sellers Rank: #425,237 in Books (See Top 100 in Books)
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Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra 2nd Edition
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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.
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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.