A History of Vector Analysis: The Evolution of the Idea of a Vectorial System (Dover Books on Mathematics)

Michael J. Crowe

ISBN 10: 0486679101 / ISBN 13: 9780486679105

Editore: Dover Publications, 2011

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Riassunto:

On October 16, 1843, 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 he 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 or 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 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 a s "a fascinating 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.

Contenuti: Chapter One THE EARLIEST TRADITIONS I. Introduction II. The Concept of the Parallelogram of Velocities and Forces III. Leibniz' Concept of a Geometry of Situation IV. The Concept of the Geometrical Representation of Complex Numbers V. Summary and Conclusion Notes Chapter Two SIR WILLIAM ROWAN HAMILTON AND QUATERNIONS I. Introduction: Hamiltonian Historiography II. Hamilton's Life and Fame III. Hamilton and Complex Numbers IV. Hamilton's Discovery of Quaternions V. Quaternions until Hamilton's Death (1865) VI. Summary and Conclusion Notes "Chapter Three OTHER EARLY VECTORIAL SYSTEMS, ESPECIALLY GRASSMANN'S THEORY OF EXTENSION" I. Introduction II. August Ferdinand Möbius and His Barycentric Calculus III. Giusto Bellavitis and His Calculus of Equipollences IV. Hermann Grassmann and His Calculus of Extension: Introduction V. Grassmann's Theorie der Ebbe und Flut VI. Grassmann's Ausdehnungslehre of 1844 VII. The Period from 1844 to 1862 VIII. "Grassmann's Ausdehnungslehre of 1862 and the Gradual, Limited Acceptance of His Work" IX. Matthew O'Brien Notes Chapter Four TRADITIONS IN VECTORIAL ANALYSIS FROM THE MIDDLE PERIOD OF ITS HISTORY I. Introduction II. Interest in Vectorial Analysis in Various Countries from 1841 to 1900 III. Peter Guthrie Tait: Advocate and Developer of Quaternions IV. Benjamin Peirce: Advocate of Quaternions in America V. James Clerk Maxwell: Critic of Quaternions VI. William Kingdom Clifford: Transition Figure Notes Chapter Five GIBBS AND HEAVISIDE AND THE DEVELOPMENT OF THE MODERN SYSTEM OF VECTOR ANALYSIS I. Introduction II. Josiah Willard Gibbs III. Gibbs' Early Work in Vector Analysis IV. Gibbs' Elements of Vector Analysis V. Gibbs' Other Work Pertaining to Vector Analysis VI. Oliver Heaviside VII. Heaviside's Electrical Papers VIII. Heaviside's Electromagnetic Theory IX. The Reception Given to Heaviside's Writings Conclusion Notes Chapter Six A STRUGGLE FOR EXISTENCE IN THE 1890'S I. Introduction II. "The "Struggle for Existence" III. Conclusions Notes CHAPTER SEVEN THE EMERGENCE OF THE MODERN SYSTEM OF VECTOR ANALYSIS: 1894-1910 I. Introduction II. Twelve Major Publications in Vector Analysis from 1894 to 1910 III. Summary and Conclusion Notes Chapter Eight SUMMARY AND CONCLUSIONS Notes Index

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Titolo: A History of Vector Analysis: The Evolution ...
Casa editrice: Dover Publications
Data di pubblicazione: 2011
Legatura: Brossura
Condizione: very_good