Basic Calculus: From Archimedes to Newton to its Role in Science

Rating:
Summary: A Website for Hahn's Basic Calculus
Review: Basic Calculus: From Archimedes to Newton to Its Role in Science
is a beautifully done text. It is very clearly written and
logically organized, tracing the development of calculus with
many interesting examples from the physical world and man's
quest to understand the physical world. The text is concise
and so readily understood as to be elegant. Finally, all of the
solutions to the exercises are given at Professor Hahn's internet
site. Its address is www.nd.edu/~hahn/ One way to remember the
website is that the letters "nd" are for Notre Dame, where Dr. Hahn teaches.

Rating:
Summary: A Website for Hahn's Basic Calculus
Review: Basic Calculus: From Archimedes to Newton to Its Role in Science
is a beautifully done text. It is very clearly written and
logically organized, tracing the development of calculus with
many interesting examples from the physical world and man's
quest to understand the physical world. The text is concise
and so readily understood as to be elegant. Finally, all of the
solutions to the exercises are given at Professor Hahn's internet
site. Its address is www.nd.edu/~hahn/ One way to remember the
website is that the letters "nd" are for Notre Dame, where Dr. Hahn teaches.

Rating:
Summary: My students enjoy "The Story of Calculus".
Review: 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.

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Summary: A really different calculus textbook.
Review: I loved this book. I find Calculus extremely intimidating and I never have quite grasped the importance of this topic. This book seems to pull things together, presents material you would not find in a "regular" text.

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Summary: Calculus Appreciation
Review: I've been wanting to learn calculus for several years now, but at 50 years old I need reasons to stuff even one new idea into an already crowded and reasonably well balanced head. I keep getting distracted looking for context: answers to the questions which always pop up in an older brain trying to make things FIT! And in the standard texts and even books for laymen I haven't been getting my questions satisfactorily answered. Until now.

Thank you Alexander J. Hahn for CONTEXT, CONTEXT, CONTEXT.

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Summary: The essence of the matter¿
Review: 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.

Rating:
Summary: A Wonderful Introduction to Calculus
Review: What this book is not is a traditional calculus text. It covers a lot of traditional topics, but not in a familiar way. It is not terribly rigorous, nor does it need to be. It is designed to fill the first two semesters of calculus. There are a LOT of books that do this in the traditional way, that is they scare the life out of the student :-). It is my belief that this book will take a lot of the mystery out of calculus, since it develops the subject in the context of applications. I also think that most students will find the approach engaging. There are plenty of practice problems at the ends of the chapters, and some are quite challenging.

The focus of this book is not to present calculus as a theory, a thing which most students are simply not prepared for at this level. Rather it is to present calculus as the pragmatic development of methods to solve certain classes of problems. In this regard it does a fantastic job. Along the way the students's algebraic, geometric, and trigonometric skills are all tested and firmed up.

The notion of the limit, such a mystery to most freshmen (and, truth-be-told, to many upper-level undergrads) is given a strong intuitive thrust right from the beginning.

If you want more problems, get the Schaum's outline book and read them side-by-side.