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

by Crowe, Michael J.

• ISBN13: 9780486679105
• ISBN10: 0486679101
• Edition: Reprint
• Format: Paperback
• Copyright: 2011-11-02
• Publisher: Dover Publications

Summary

The first large-scale study of the development of vectorial systems, awarded a special prize for excellence in 1992 from France's 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. 1985 corrected edition of 1967 original.

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