History of Vector Analysis

The Evolution of the Idea of a Vectorial System

Häftad, Engelska, 2003

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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.

Produktinformation

Utgivningsdatum2003-03-28
Mått140 x 220 x 30 mm
Vikt310 g
FormatHäftad
SpråkEngelska
SerieDover Books on Mathema 1.4tics
Antal sidor304
FörlagDover Publications Inc.
ISBN9780486679105

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Beräkning och matematisk analys inom Naturvetenskap och teknik

Chapter One THE EARLIEST TRADITIONSI. IntroductionII. The Concept of the Parallelogram of Velocities and ForcesIII. Leibniz' Concept of a Geometry of SituationIV. The Concept of the Geometrical Representation of Complex NumbersV. Summary and ConclusionNotesChapter Two SIR WILLIAM ROWAN HAMILTON AND QUATERNIONSI. Introduction: Hamiltonian HistoriographyII. Hamilton's Life and FameIII. Hamilton and Complex NumbersIV. Hamilton's Discovery of QuaternionsV. Quaternions until Hamilton's Death (1865)VI. Summary and ConclusionNotes"Chapter Three OTHER EARLY VECTORIAL SYSTEMS, ESPECIALLY GRASSMANN'S THEORY OF EXTENSION"I. IntroductionII. August Ferdinand Möbius and His Barycentric CalculusIII. Giusto Bellavitis and His Calculus of EquipollencesIV. Hermann Grassmann and His Calculus of Extension: IntroductionV. Grassmann's Theorie der Ebbe und FlutVI. Grassmann's Ausdehnungslehre of 1844VII. The Period from 1844 to 1862VIII. "Grassmann's Ausdehnungslehre of 1862 and the Gradual, Limited Acceptance of His Work"IX. Matthew O'Brien NotesChapter Four TRADITIONS IN VECTORIAL ANALYSIS FROM THE MIDDLE PERIOD OF ITS HISTORYI. IntroductionII. Interest in Vectorial Analysis in Various Countries from 1841 to 1900III. Peter Guthrie Tait: Advocate and Developer of QuaternionsIV. Benjamin Peirce: Advocate of Quaternions in AmericaV. James Clerk Maxwell: Critic of QuaternionsVI. William Kingdom Clifford: Transition Figure NotesChapter Five GIBBS AND HEAVISIDE AND THE DEVELOPMENT OF THE MODERN SYSTEM OF VECTOR ANALYSISI. IntroductionII. Josiah Willard GibbsIII. Gibbs' Early Work in Vector AnalysisIV. Gibbs' Elements of Vector AnalysisV. Gibbs' Other Work Pertaining to Vector AnalysisVI. Oliver HeavisideVII. Heaviside's Electrical PapersVIII. Heaviside's Electromagnetic TheoryIX. The Reception Given to Heaviside's WritingsConclusionNotesChapter Six A STRUGGLE FOR EXISTENCE IN THE 1890'SI. IntroductionII. "The "Struggle for Existence"III. ConclusionsNotesCHAPTER SEVEN THE EMERGENCE OF THE MODERN SYSTEM OF VECTOR ANALYSIS: 1894-1910I. IntroductionII. Twelve Major Publications in Vector Analysis from 1894 to 1910III. Summary and ConclusionNotesChapter Eight SUMMARY AND CONCLUSIONSNotesIndex