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A History of Vector Analysis: The Evolution of the Idea of a Vectorial System

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A History of Vector Analysis: The Evolution of the Idea of a Vectorial System Cover

 

Synopses & Reviews

Publisher Comments:

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.

Synopsis:

Prize-winning study traces the rise of the vector concept from the discovery of complex numbers through the systems of hypercomplex numbers to the final acceptance around 1910 of the modern system of vector analysis.

Synopsis:

The first large-scale study of the development of vectorial systems, awarded a special prize for excellence in 1992 from Frances prestigious Jean Scott Foundation. 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. Concentrates on vector addition and subtraction, the forms of vector multiplication, vector division (in those systems where it occurs), and the specification of vector types.

Table of Contents

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

Product Details

ISBN:
9780486679105
Author:
Crowe, Michael J.
Publisher:
Dover Publications
Author:
Mathematics
Subject:
General
Subject:
History
Subject:
Mathematics
Subject:
Calculus
Subject:
Vector Analysis
Subject:
Vector analysis -- History.
Subject:
General Mathematics
Subject:
Hisotory of Mathematics
Subject:
Quaternions
Subject:
Mathematics-Calculus
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Series Volume:
no. 147
Publication Date:
20111131
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
304
Dimensions:
8.5 x 5.38 in 0.71 lb

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Related Subjects


Science and Mathematics » Mathematics » Calculus » General
Science and Mathematics » Mathematics » History
Science and Mathematics » Mathematics » Vector Analysis

A History of Vector Analysis: The Evolution of the Idea of a Vectorial System New Trade Paper
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Product details 304 pages Dover Publications - English 9780486679105 Reviews:
"Synopsis" by ,
Prize-winning study traces the rise of the vector concept from the discovery of complex numbers through the systems of hypercomplex numbers to the final acceptance around 1910 of the modern system of vector analysis.
"Synopsis" by ,
The first large-scale study of the development of vectorial systems, awarded a special prize for excellence in 1992 from Frances prestigious Jean Scott Foundation. 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. Concentrates on vector addition and subtraction, the forms of vector multiplication, vector division (in those systems where it occurs), and the specification of vector types.
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