- 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: 58 customer reviews
- Amazon Best Sellers Rank: #263,304 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 had the privilege of learning Calculus from the author himself at Caltech, using these books of course. Though I took it shortly before Apostol retired, his lectures were precision masterpieces in clearly laid out mathematical prose. Just like the books. I looked forward to his classes every week. The same blue-striped shirt and blue pants he wore every day (always super-clean -- I never figured out whether he had a bunch of them or had them laundered every time). The beads of sweat on his brow the day we played a prank on him and made the clock run faster, shorting him 10 minutes of his well-orchestrated lecture. But I digress. The important thing is that the learning from this book extends beyond Calculus. Once you make the investment in how to learn math from this book, you will have obtained a valuable tool for life. This book actually deserves 6 stars.
I want to give this book 5 stars, but I'm not sure that I can just because I can't pin down whether or not this book achieves more than Spivak in the way of explaining the whys of everything completely. I will say, however, that this book is probably better than even intro analysis texts such as Ross's Elementry Analysis. And I do really like, and prefer, how this book explains both intuition and formal justification (nearly fully, see the end of this paragraph). I actually think one without the other is fruitless because too much rigour actually leads you to the fact that, unfortunately, due to Russel's paradox, all of mathematics *can't* be explained away by pure logic and reason alone, and that's where what is called intuition and induction really does become all that's left in explaining things. So, the point is that Spivak drops the ball by leading people to believe everything can confidently be reasoned out, but, the other main point of this paragraph is that Apostle still left me with questions on the definition of limits, and specifically, I found that he did not explain clearly enough one-sided limits in terms of epsilon-deltas and even more specifically, he did not show us how to determine if a limit exists using epsilon-delta arguments in practice (I haven't read the sequences and series section yet though, so it may show up here -- full disclousre). If Apostle just added in this little bit more to the book it would be perfect and warrant a 5-star rating.
The book has several strengths. The first is that it is readable (for a math book). I have caught myself reading it when I should be preparing lessons. Rather than a stream of examples, the author takes time to explain the theory, the proofs, and the basic concepts. The second strength is that the author is thorough. Theorems are proven and the reader can truly see why we do the things we do in Calculus. Rather than just give a list of integration techniques, the reader sees where they come from. The final big strength is organization.
This book is organized differently from the typical text. The author begins with integration, switches to derivatives, and then back to integration. I realized that this was a good idea, especially in my situation. If I get through the first few chapters, I'll have covered the basic concepts of integration and derivatives. If I go further, I'll have covered many of the advanced techniques. I'm not certain why he chose this order, but it works well for me and, apparently, it is historical. (In high school I don't use the latter half of the book. I essentially cover Calculus I over a full year.)
The obvious question is why I chose this as a high school book. As I noted, I was not satisfied with the "official" text, so I sought a cheap alternative. I was able to pick up almost enough copies of this book in a cheap used version for my class. It was acceptable because of the strengths I mentioned. I've had to skip topics and simplify topics for my high school students, but the difference I'm seeing, so far, is night and day. These students are far less frustrated than last year and they're understanding the material far better. It's likely my teaching has improved, but I have to give most of the credit to this textbook. It is something special when high school students can understand an advanced college book.
Ideally, I would love to find a high school version of this book. It is a great book!