|Title||A History of Vector Analysis|
|Author(s)||Michael J. Crowe|
|Description||The Evolution of the Idea of a Vectorial System
On October 16, 1943, Sir William Rowan Hamilton discovered quaternions and, on the very same day, presented his breakthrough to the Royal Irish Academy. Meanwhile, in a less dramatic style, a German high school teacher, Hermann Grassmann, was developing another vectorial system involving hypercomplex numbers comparable to quaternions. The creations of these two mathematicians led to other vectorial systems, most notably, the system of vector analysis formulated by Josiah Willard Gibbs and Oliver Heaviside and now almost universally employed in mathematics, physics, and engineering. Yet the Gibbs-Heaviside system won acceptance only after decades of debate and controversy in the latter half of the nineteenth century concerning which of the competing systems offered the greatest advantages for mathematical pedagogy and practice.
This volume, the first large-scale study of the development of vectorial systems, traces the rise of the vector concept from the discovery of complex numbers through the systems of hypercomplex numbers created by Hamilton and Grassmann to the final acceptance around 1910 of the modern system of vector analysis. Professor Michael J. Crowe (University of Notre Dame) discusses each major vectorial system as well as the motivations that led to their creation, development, and acceptance of rejection.
The vectorial approach revolutionized mathematical methods and teaching in algebra, geometry, and physical science. As Professor Crowe explains, in these areas traditional Cartesian methods were replaced by vectorial approaches. He also presents the history of the ideas of vector addition, subtraction, multiplication, division (in those systems where it occurs), and differentiation. His book also contains refreshing portraits of the personalities involved in the competition among the various systems.
Teachers, students, and practitioners of mathematics, physics, and engineering as well as anyone interested in the history of scientific ideas will find this volume to be well written, solidly argued, and excellently documented. Reviewers have described it as "a fascinated volume," "an engaging and penetrating historical study" and "an outstanding book [that] will doubtless long remain the standard work on the subject." In 1992 it won an award for excellence from the Jean Scott Foundation of France.
|Dedication||"TO MARY ELLEN"|
|Book Dimensions||Width: 5.5″ (5 ½″)|
|Height: 8.5″ (8 ½″)|
|Depth: 0.63″ (5/8;″)|
|Contents||Chapter One The Earliest Traditions, Chapter Two Sir William Rowan Hamilton and Quaternions, Chapter Three Other Early Vectorial Systems Especially Grassmann's Theory Of Extension, Chapter Four Traditions In Vectorial Analysis From The Middle Period Of Its History, Chapter Five Gibbs And Heaviside And The Development Of The Modern System Of Vector Analysis, Chapter Six A Struggle For Existence In The 1890s, Chapter Seven The Emergence of the Modern System of Vector Analysis: 1894-1910, Chapter Eight Summary and Conclusions, Index|
|Cover Design||Paul E. Kennedy|
|Published||November 2, 2011 (Reprint edition)|
|Publisher||Dover Publications (www.doverpublications.com).|
|Manufactured in||United States of America. Dover Publications, Inc. 180 Varick Street New York, N.Y. 10014|
|Copyright||© 1967 by University of Notre Dame Press. New material copyright © 1985 by Michael J. Crowe. All Rights Reserved.|
|Book Format||Kindle, Hardcover, Paperback|
|Best Seller's List||--|
|Other||Dover republication of the edition originally published by Henry Holt & Co., New York, 1911.|
|Library of Congress
|1. Vector analysis—History.|
|LC Control Number||????|
|LC Call Number||QA433.C76 1993|
|DDC Call Number||515″.63—dc20|