Approximately Calculus [Hardcover]

Shahriar Shahriari (Author)

Book Description

ISBN-10: 0821837508 | ISBN-13: 978-0821837504 | Publication Date: December 12, 2006

Is there always a prime number between $n$ and $2n$? Where, approximately, is the millionth prime? And just what does calculus have to do with answering either of these questions? It turns out that calculus has a lot to do with both questions, as this book can show you. The theme of the book is approximations. Calculus is a powerful tool because it allows us to approximate complicated functions with simpler ones. Indeed, replacing a function locally with a linear--or higher order--approximation is at the heart of calculus. The real star of the book, though, is the task of approximating the number of primes up to a number $x$. This leads to the famous Prime Number Theorem--and to the answers to the two questions about primes. While emphasizing the role of approximations in calculus, most major topics are addressed, such as derivatives, integrals, the Fundamental Theorem of Calculus, sequences, series, and so on. However, our particular point of view also leads us to many unusual topics: curvature, Padé approximations, public key cryptography, and an analysis of the logistic equation, to name a few. The reader takes an active role in developing the material by solving problems. Most topics are broken down into a series of manageable problems, which guide you to an understanding of the important ideas. There is also ample exposition to fill in background material and to get you thinking appropriately about the concepts. Approximately Calculus is intended for the reader who has already had an introduction to calculus, but wants to engage the concepts and ideas at a deeper level. It is suitable as a text for an honors or alternative second semester calculus course.

Editorial Reviews

Review

This fascinating book is a novel approach to undergraduate analysis, which combines most topics in single variable calculus with some elementary number theory. ... It is very well written and fully engages readers in its developments, often beginning with examples and leading them to develop generalizations and, ultimately, theorems and proofs. ... An attractive book, well worth consulting for ideas on presenting topics, or for examples. ---- J.H. Ellison, Choice

The book is very well written and contains many references to articles in journals that are accessible to students ... ---- MAA Reviews

Product Details

• Hardcover: 292 pages
• Publisher: American Mathematical Society (December 12, 2006)
• Language: English
• ISBN-10: 0821837508
• ISBN-13: 978-0821837504
• Product Dimensions: 10.2 x 7.2 x 0.8 inches
• Shipping Weight: 1.5 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #1,096,413 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

1 of 1 people found the following review helpful:

5.0 out of 5 stars Fun, November 26, 2010

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Sragain17 - See all my reviews

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This review is from: Approximately Calculus (Hardcover)

Probably the most educational math book ever. Instructor not included, but often required. This is probably the manliest calculus book ever written- the faint-hearted need not purchase. This book will teach you calculus forwards instead of backwards, i.e. you'll solve the problems before learning the theorem.

2 of 3 people found the following review helpful:

5.0 out of 5 stars Good book with many hard problems, October 2, 2008

By 

Uday Karan Singh - See all my reviews
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This review is from: Approximately Calculus (Hardcover)

Explores Calculus in a novel way. Has many good calculus questions and some elementary number theory problems as well. Only drawback is that its impossible to find the solutions to the problems in the book.