A History of Vector Analysis

"A History of VECTOR ANALYSIS" (1967) is a book on the history of gibbsian vector analysis [ [http://books.google.com/books?id=G_uTYAgutXAC&pg=PA96&lpg=PA96&dq=%22Gibbsian+Vector+Analysis%22&source=web&ots=-rorwcas9x&sig=SDQflbWVni-PE-Ev5wgPL7rhr18&hl=en Differential Forms in Electromagnetics By Ismo V. Lindell, Wiley-IEEE 2004, 253 pages] ISBN 0-4716-4801-9 ] [ [http://www.newyorker.com/archive/2006/11/27/061127crbo_books "Do the Math: Thomas Pynchon returns" by Louis Menand, The New Yorker November 27, 2006] ] [ [http://www.springerlink.com/content/bb35nu5waxyq4l6x/ Helmholtz Theorem For Multiform Fields by V. Lindell and G. Dassios, Journal of Electromagnetic Waves and Applications, Volume 17, Number 1 / January, 2003] ] by Michael J. Crowe, originally published by the University of Notre Dame Press. Despite receiving a certain amount of criticism [ [http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.bams/1183533587 Review: ...Michael J. Crowe, A History of Vector Analysis...by William C. Waterhouse Source: Bull. Amer. Math. Soc. Volume 78, Number 3 (1972), 385-391.] ] when first published, it has since garnered praise, in particular by being recognized by Maison des Sciences de l'Homme's [ [http://www.msh-paris.fr/index.php?id=1&L=1 Maison des Sciences de l'Homme's Website] ] Jean Scott Foundation in late 1992. [ [http://books.google.com/books?id=g0T8hPo7i-4C&pg=PR3&lpg=PR3&dq=a+history+of+vector+analysis+scott&source=web&ots=ViNcRkKX7g&sig=hXwB73aZmFSXGeWBbQ6BA946P4g&hl=en A History of Vector Analysis (Dover preview)] ]

ummary of book

The book has eight chapters. The first on the origins of gibbsian vector analysis including Ancient Greek and 16th and 17th century influences. The second on the 19th century William Rowan Hamilton and Quaternions. The third on other 19th and 18th century vectorial systems. The fourth on the general interest in the 19th century on vectorial systems including analysis of journal publications as well as sections on major figures and their views (e.g., Peter Guthrie Tait as an advocate of Quaternions and James Clerk Maxwell as a critic of Quaternions). The fifth on Josiah Willard Gibbs and Oliver Heaviside and their development of a modern system of vector analysis. The sixth on the major debates of the 1890's in trying to reach an international consensus on a standard vectorial system. The seventh on the emergence of a modern vector analysis system in the 1894-1910 period, particularly with the 1901 publication of Vector Analysis (Gibbs/Wilson). The eighth is the author's summary and conclusions. [ Quote from page ix, "Concerning bibliography. No formal bibliographical section has been included in this book. The reader will find however that the sections of notes at the end of each chapter will serve rather well as a bibliography for that chapter. Moreover the need for a bibliography is greatly diminished by the existence of a book that lists nearly all relevant primary documents published to about 1912." ] The book relies on references in chapter endnotes instead a bibliography section. Crowe also states that a bibliography compiled in 1912 already lists all the primary literature for the study

ummary of reviews

There were significant reviews given near the time of original publication. Morris Kline begins his 1969 review with "Since historical publications on modern developments are rare, this book is welcome." and ends with "the subtitle is a better description of the contents than the title proper." Then William Waterhouse--picking up where Kline's review left off--writes in 1972 "Crowe's book on vector analysis seems a little anemic in comparison, perhaps because its title is misleading. ... [Crowe] does succeed in his goal of tracing the genealogy of the 3-space system, concluding that it was developed out of quaternions by physicists."

References

*A History of Vector Analysis: The Evolution of the Idea of a Vectorial System. Michael J. Crowe, University of Notre Dame Press 1967, pages xvii, 270. ASIN: B000GX2E78
* [http://www.amazon.com/dp/0486679101 A History of Vector Analysis: The Evolution of the Idea of a Vectorial System.] Michael J. Crowe, Dover Publications 1994, pages 288. ISBN: 0-4866-7910-1
*Review of A History of Vector Analysis "Mathematical Reviews" Morris Kline, 37 #5070, 1969.
*William C. Waterhouse, "Bulletin American Mathematics Society", Volume 78, Number 3 (1972), 385-391.
* [http://web.archive.org/web/20040410112349/www.nku.edu/~curtin/crowe_oresme.pdf M.J. Crowe speaks at U. Louisville, 2002]

Notes