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Title: A History of Vector Analysis : The Evolution of the Idea of a Vectorial System by Michael J. Crowe ISBN: 0-486-67910-1 Publisher: Dover Pubns Pub. Date: February, 1994 Format: Paperback Volumes: 1 List Price(USD): $12.95 |
Average Customer Rating: 4.5 (2 reviews)
Rating: 4
Summary: Thoughtful, Detailed History of Vector Analysis
Comment: How were the concepts of vector analysis developed? How did modern vector notation become widely accepted? Who were the key players and why did quaternions fail to gain acceptance? This book is extensively documented, scholarly in its approach, sometimes a bit slow, but overall it is a fascinating look at these specific questions as well as the fundamental issue of what factors promote or delay acceptance of revolutionary ideas in science and mathematics.
I did not become immediately engaged with Crowe's style and even set the book aside after reading the prefaces and first chapter. A few months later I returned to chapter two (in part due to a previous reviewer's high rating). And what a surprise - I suddenly found myself intrigued with Crowe's discussion of Sir William Hamilton's single minded focus on quaternions, the perseverance and genius of Hermann Grassmann, the critical roles played by Peter Tait and James Maxwell, and the pragmatic way in which Josiah Gibbs and Oliver Heaviside independently extracted key vectorial concepts from Hamiliton-Tait's quaternion analysis.
Crowe's book was originally published in 1967 by University of Notre Dame, Dover reprinted it in 1985, Crowe recieved the Jean Scott Prize by the Maison des Sciences de l'Homme (Paris)in 1992, and Dover reprinted it again in 1992. Dover should be commended for making such reprints readily available at affordable prices.
The discussion of Hamilton's quaternions does not require familiarity with quaternions, but some prior acquaintance might be helpful. I encountered quaternions in another Dover reprint: Matrices and Transformations by Pettofrezzo. Section 2-3 introduces quaternion notation, simple manipulations, and shows that addition and multiplication of quaternions is isomorphic with two particular sets of matrices.
Has quaternion analysis survived? See Quaternions and Rotation Sequences: A Primer With Applications to Orbits, Aerospace, and Virtual Reality by Jack Kuipers, Aprill, 1999. The reviews by readers are all five stars.
Rating: 5
Summary: Thorough, intelligent and impeccably unprejudiced.
Comment: This book is a model of science history. Crowe manages to give one a clear view of the trends and moods of the time (1840-1900), the personalities of the various figures involved (Esp. Hamilton, Grassman and Gibbs), without sacrificing his most significant asset: the facts.
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Title: The History of the Calculus and Its Conceptual Development by Carl B. Boyer ISBN: 0486605094 Publisher: Dover Pubns Pub. Date: September, 1980 List Price(USD): $11.95 |
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Title: Div, Grad, Curl, and All That: An Informal Text on Vector Calculus by Harry M. Schey ISBN: 0393969975 Publisher: W.W. Norton & Company Pub. Date: August, 1997 List Price(USD): $17.95 |
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Title: Geometrical Vectors (Chicago Lectures in Physics) by Gabriel Weinreich ISBN: 0226890481 Publisher: University of Chicago Press Pub. Date: July, 1998 List Price(USD): $17.50 |
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Title: Gamma: Exploring Euler's Constant by Julian Havil, Freeman Dyson ISBN: 0691099839 Publisher: Princeton Univ Pr Pub. Date: May, 2003 List Price(USD): $29.95 |
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Title: Abel's Proof : An Essay on the Sources and Meaning of Mathematical Unsolvability by Peter Pesic ISBN: 0262162164 Publisher: MIT Press Pub. Date: June, 2003 List Price(USD): $24.95 |
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