Basic Calculus: From Archimedes to Newton to its Role in Science [Hardcover]

Alexander J. Hahn (Author)

Book Description

ISBN-10: 0387946063 | ISBN-13: 978-0387946061 | Publication Date: July 17, 1998 | Edition: 1

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.

Product Details

• Hardcover: 546 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: 4.0 out of 5 stars  See all reviews (13 customer reviews)
• Amazon Best Sellers Rank: #891,187 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

19 of 19 people found the following review helpful:

5.0 out of 5 stars My students enjoy "The Story of Calculus"., January 18, 2001

By 

Satoru S. Kano (Tokyo, Japan) - See all my reviews

This review is from: Basic Calculus: From Archimedes to Newton to its Role in Science (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.

Of course, "the emphasis is always on the careful development of the mathematics and information that it provides", and most of the topics of first-year calculus courses (including differential equations) are covered (but partial differentials and double/triple integrals are not). The exercise section of each chapter contains advanced explanations of historical, scientific, and mathematical topics, and is organically integrated with the text. The total number of the problems in all the 15 chapters is close to 700. With its many figures and illustrations, as well as full derivations of the equations, this text is also suitable as a supplementary or a self-study manual.

I strongly recommend Basic Calculus to those who have doubts about "the usual math training" which sometimes makes us feel like machines (not humans), as a rare and engaging view of mathematics from a different angle. I have found the contents of Hahn's textbook ideal for my students in general physics and calculus courses at Hosei University, Tokyo, and I am now completing a translation of this book into Japanese in collaboration with my colleague Professor Ichimura.

19 of 20 people found the following review helpful:

5.0 out of 5 stars The essence of the matter, August 2, 2000

By 

"clarkphx" (Tempe, AZ USA) - See all my reviews

This review is from: Basic Calculus: From Archimedes to Newton to its Role in Science (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: [e-mail]

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.

17 of 19 people found the following review helpful:

5.0 out of 5 stars Basic Calculus, September 7, 2000

By A Customer

This review is from: Basic Calculus: From Archimedes to Newton to its Role in Science (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.