Basic Calculus: From Archimedes to Newton to its Role in Science (Textbooks in Mathematical Sciences) 1st Edition

by Alexander J. Hahn (Author)

12 customer reviews

ISBN-13: 978-0387946061

ISBN-10: 0387946063

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This introductory calculus text was developed by the author through his teaching of an honors calculus course at Notre Dame. The book develops calculus, as well as the necessary trigonometry and analytic geometry, from witin the relevant historical context, and yet it is not a textbook in the history of mathematics as such. The notation is modern, and the material is selected to cover the basics of the subject. Special emphasis is placed on pedagogy throughout. Whhile emphasizing the broad applications of the subject, emphasis is placed on the mathematical content of the subject.

Basic Calculus: From Archimedes to Newton to its Role in Science (Textbooks in Mathematical Sciences)

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Product Details

Series: Textbooks in Mathematical Sciences
Hardcover: 545 pages
Publisher: Key College; 1 edition (July 17, 1998)
Language: English
ISBN-10: 0387946063
ISBN-13: 978-0387946061
Product Dimensions: 10 x 8.6 x 1.2 inches
Shipping Weight: 3.4 pounds
Average Customer Review: 4.2 out of 5 stars See all reviews (12 customer reviews)
Amazon Best Sellers Rank: #1,053,213 in Books (See Top 100 in Books)
- #209 in Books > Science & Math > Mathematics > Pure Mathematics > Functional Analysis
- #723 in Books > Science & Math > Mathematics > Mathematical Analysis
- #846 in Books > Science & Math > Mathematics > History

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Customer Reviews

4.3 out of 5 stars

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4 star		17%
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2 star		8%
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23 of 25 people found the following review helpful

My students enjoy "The Story of Calculus".

By Satoru S. Kano on January 18, 2001

Format: Hardcover

How can we say that introductory courses in calculus at universities are meaningful if the students are never involved in math as professionals? What motivation can we offer them for studying it? This textbook, by Alexander J. Hahn, provides an outstanding answer to the question backed up by the author's precious teaching experience at the University of Notre Dame.
After reading the text, the reader will start to see calculus as a gift by our ancestors that helps us to analyze practical daily problems: calculus as a culture to be passed on to the next generation. Firstly, as the author says, "this text could as well have the title The Story of Calculus." As we read it, we find ourselves reliving history with the great persons like Archimedes, Descartes, Leibniz and Newton. We feel the activity and wisdom of the characters close-up, and we even experience their joys and sorrows as if they were our own. In a way, this book is a historical novel. It shows what calculus looks like as a critical tool that has helped to clear up the mysteries of the universe. Secondly, "the purpose of this text is to demonstrate its broad and formidable informative power." As the author explains, calculus enables us to designing telescopes, to read nuclear clocks, to design suspension bridges, and to understand the interior ballistics of rifles, the rocket equation, gravity, and the expanding universe. Economic subjects, such as banking, CPI, market mechanisms, cost analysis are also covered with full explanations. Books with such range and depth are rare indeed. It is easy to understand why the author received an award for teaching excellence.Read more ›

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21 of 23 people found the following review helpful

The essence of the matter�

By whatever on August 2, 2000

Format: Hardcover

If you are deeply curious about the amazing ability of mathematics to define, describe and predict the physical world and its behavior (incl. the solar system) you will be thrilled with this book. It concentrates on the essence of the matter, basic calculus, and includes real-world applications set within the context of some of history's most important scientific questions.
The author clearly demonstrates that he not only possesses a great curiosity, fluency, and appreciation for the subject but also thrives on imparting these things to others. He has provided a great deal of supplementary information on his web site including a detailed description of the contents, scope and focus of the book.
The Solution Manuals ARE available from the author simply by e-mailing him at: hahn.1@nd.edu
Most calculus books make some compromise in presenting the material. In the case of a thoroughly rigorous text, that compromise most often means sacrificing historical context, intuitive understanding, and real-world application (even though the book may be "exercise-rich" with contrived examples). Basic Calculus successfully navigates a difficult (and different) course, focusing on these commonly sacrificed areas and effectively presenting the pearls of calculus knowledge without delving too deeply into eye-glazing minutiae. In lucid and interesting style, it accomplishes exactly what it sets out to do - it imparts the essence of the matter, in context.

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19 of 21 people found the following review helpful

Basic Calculus

By A Customer on September 7, 2000

Format: Hardcover

This splendid book aims to develop calculus from within its rich historical context and to demonstrate its power across a range of disciplines. The author succeeds admirably. Two hundred pages devoted to key ideas in the history of mathematics and science lead smoothly into calculus as we know it today. The remaining three hundred plus pages cover the usual topics, but with attention given to an extraordinary spread of interesting problems in science and business. The explanations of concepts and notation are as lucid as any I have encountered in a basic calculus book.
Because one of the distinguishing features of Basic Calculus from Archimedes to Newton to its Role in Science is its historical dimension, something should be said about the criticism of one reviewer that the book oversimplifies the history by using modern notation. Yes, Hahn does tidy things up. (Very nicely, I might add.) But what else can anyone really do? As Hahn notes, Leibniz's cryptic first work on calculus - Nova methodus pro maximis et minimis, itemque tangentibus...calculi genus - bewildered even his friends, the brothers Bernoulli. These famous mathematicians found Leibniz's article "an enigma rather than an explication." Hahn could try to unriddle the Nova methodus for us, explaining in detail all the fuzzy concepts and strange notation that baffled the Bernoullis. But that hardly seems the thing to do in a basic calculus book. Better to do just what Hahn does - seize on the essential ideas and use everything now at a mathematician's command to bring them into a clear light. Hahn has an excellent sense of just how far to go. The result is a truly extraordinary book that will amply reward readers looking for something special.

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13 of 14 people found the following review helpful

This book succeeds in its important goals.

By A Customer on November 24, 1998

Format: Hardcover

If you want a sound understanding and appreciation of basic calculus, have a look at Alexander Hahn's "Basic Calculus". An author presenting calculus could seek to impart (A) Proficiency in its techniques, (B) Justification of its methods, (C) Understanding of its principles or (D) Appreciation of its significance in the history of mathematics and science. Many pre-engineering calculus texts do a good job of drilling proficiency and building an appreciation of calculus by showing its utility in scientific applications. It is, however, easy to walk away from a pre-engineering calculus course without an intuitive grasp of the subject, or any sense of why calculus is important in the history of thought. There are also many mathematically oriented calculus texts that present the logical structure of calculus very well. These books stress precise concepts and proofs that were actually developed after calculus had revolutionized the physical sciences. Since the precise justification was developed after the fact, it is clear that one can understand the concepts without understanding the justification. Unfortunately many of formal calculus texts also show that it is possible to understand the justification (follow the proofs) without an understanding of the subject matter. History of mathematics books can convey an appreciation of why calculus was a great intellectual achievement, but they often tell the reader very little about the mathematics itself. There are many fewer books that attempt to convey an understanding of calculus and an appreciation of its significance in the history of mathematics and in science. Hahn's book addresses this neglected area.
Hahn's book has two parts, "From Archimedes to Newton" and "Calculus and the Sciences".Read more ›

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Most Recent Customer Reviews

A Website for Hahn's Basic Calculus

Basic Calculus: From Archimedes to Newton to Its Role in Science
is a beautifully done text. It is very clearly written and
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A really different calculus textbook.

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Published on November 1, 1999 by Janice Stewart (jstew@siu.edu)

Not what I expected...

This book wasn't what I had expected. My expectations were failed in 3 ways: 1. I expected the book to give full proofs for all examples. 2. Read more

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It's a lovely book. What's especially nice about it is how it places calculus firmly in the world, first by embedding it in history and second by showing that its purpose is to... Read more

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