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A History of Vector Analysis


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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 Mobius 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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