A History of Vector Analysis: The Evolution of the Idea of a ...
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A History of Vector Analysis: The Evolution of the Idea of a Vectorial System (
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A History of Vector Analysis - Dover Publications
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A History of Vector Analysis: The Evolution of the Idea of a Vectorial System. A History of Vector Analysis: The Evolution of the Idea of a Vectorial System.
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[PDF]A History of Vector Analysis - UC Davis Mathematics
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University of California, Davis
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by MJ Crowe - Cited by 11 - Related articles
Sep 24, 2008 - A History of Vector Analysis. Michael J. Crowe. Distinguished Scholar in Residence. Liberal Studies Program and Department of Mathematics.A History of Vector Analysis - Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/A_History_of_Vector_Analysis
A History of Vector Analysis (1967) is a book on the history of vector analysis by Michael J. Crowe, originally published by the University of Notre Dame Press.
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[PDF]A Historical Study of Vector Analysis - Deep Blue
deepblue.lib.umich.edu/.../bad1474.0001...
University of Michigan Library
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by CT Tai - 1995 - Cited by 4 - Related articles
2.1 Past and Present Notations in Vector Analysis ..................... 4. 2.2 Quaternion .... In a book on the history of vector analysis [1], Michael J . Crowe made a very ...History of Vectors - McGill University
www.math.mcgill.ca/labute/courses/.../VectorHistory.ht...
The parallelogram law for the addition of vectors is so intuitive that its origin is .... good deal of modern matrix and linear algebra and vector and tensor analysis.
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History Of Vector Analysis
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ISBN 0486679101. "A History Of Vector Analysis"; by Michael J. Crowe,; University of Notre Dame Press, 1967. This book describes the history of not only Vector ...A History of Vector Analysis - Google Books
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He also presents the history of ideas of vector addition, subtraction, multiplication, ... A History of Vector Analysis: The Evolution of the Idea of a Vectorial System.
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A History of Vector Analysis:The Evolution of the Idea of a ...
www.maa.org/.../a-history-of-vecto...
Mathematical Association of America
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by MJ Crowe
Apr 14, 2012 - In 1679, Leibnitz expressed the need for a 'geometry of situation' that would be independent of the geometry of magnitude. It seems that he was ...History of Vector Analysis - Physics Forums
www.physicsforums.com › Mathematics › Calculus
May 12, 2014 - 7 posts - 5 authors
I'm quite interested in the history behind vector analysis especially Curl and Divergence and gradient operators etc. When James Maxwell ...
History of Vector Analysis May 12, 2014 #1 cooev769 114 (adsbygoogle = window.adsbygoogle || []).push({}); I'm quite interested in the history behind vector analysis especially Curl and Divergence and gradient operators etc. When James Maxwell derived Maxwell's equations of electromagnetism where these sorts of operations well known and commonly used, or are they modern fabrications. Did Maxwell actually derive his equations using the methods we use today or some other methods? Phys.org - latest science and technology news stories on Phys.org • Experian says 15M have info stolen in hack of T-Mobile data • New polymer creates safer fuels • Pluto's big moon Charon reveals a colorful and violent history May 12, 2014 #2 micromass 19,784 Staff Emeritus Science Advisor Education Advisor Insights Author (adsbygoogle = window.adsbygoogle || []).push({}); You should like this book: http://www.amazon.com/History-Vector-Analysis-Evolution-Mathematics/dp/0486679101 May 12, 2014 #3 jedishrfu 5,221 Staff: Mentor (adsbygoogle = window.adsbygoogle || []).push({}); There's a book of the subject: http://en.wikipedia.org/wiki/A_History_of_Vector_Analysis and at Amazon as a Dover publication: http://www.amazon.com/History-Vecto...95&sr=8-1&keywords=history+of+vector+analysis Vector analysis grew out of the relative complexity of using quaternions. Hamilton was trying to extend complex numbers into a new kind of number and that's where the i,j,k unit vector idea came from: a + bi + cj + dk For the divergence there's a history of the divergence theorem: http://www.sciencedirect.com/science/article/pii/0315086078902124 The curl must have been recognized and came out of similar theorems. May 12, 2014 #4 SteamKing 10,274 Staff Emeritus Science Advisor Homework Helper cooev769 said: ↑ I'm quite interested in the history behind vector analysis especially Curl and Divergence and gradient operators etc. When James Maxwell derived Maxwell's equations of electromagnetism where these sorts of operations well known and commonly used, or are they modern fabrications. Did Maxwell actually derive his equations using the methods we use today or some other methods? You can see for yourself. Maxwell's treatise on electricity and magnetism can be found at the Internet Archive: http://archive.org/search.php?query=creator:"Maxwell, James Clerk, 1831-1879" Maxwell worked with differentials and integrals, as modern vector notation had not been developed. Most of what Maxwell used in his work were quaternions. Modern vector analysis was developed by Josiah Willard Gibbs in the 1870s to simplify having to deal with quaternions and to provide more facility for his students in understanding vector concepts (When was the last time a professor went out of his way to simplify things?) May 20, 2014 #5 D H 15,558 Staff: Mentor SteamKing said: ↑ Maxwell worked with differentials and integrals, as modern vector notation had not been developed. Most of what Maxwell used in his work were quaternions. The first sentence is correct, but the second is not. It has become an internet meme, favored by crackpots who like to imagine that the vector notation used at intermediate college level hides some of Tesla's key discoveries (whatever!). Maxwell's original work, published in 1861 and 1862 as On Physical Lines of Force did not use vectors or quaternions. Nor did his Dynamical Theory of the Electromagnetic Field, published in 1864 and 1865. His original development of his theory followed the painstaking style of only using scalar equations that were in near universal use at the time. The mathematics to simplify the notation didn't exist. He did mention quaternions in passing in his final book on the subject, A Treatise on Electricity and Magnetism, published in 1873. But that was in passing, where he discussed interesting developments by others in extending his work. Maxwell himself did not use quaternions in the development of his theory. May 20, 2014 #6 SteamKing 10,274 Staff Emeritus Science Advisor Homework Helper Perhaps I was over generous in describing the extent of the use of quaternions by Maxwell in Electricity and Magnetism, but he did provide equivalent expressions for some of his results using quaternions. That modern crackpots may have a bone to pick because Maxwell did or did not use quaternions in the manner they believe he should have used them is neither here nor there. May 20, 2014 #7 D H 15,558 Staff: Mentor Yes, Maxwell did demonstrate the use of quaternions on some of his results in A Treatise on Electricity and Magnetism, but that is not what he used to develop them. He published that book near the end of his life. He spent a good deal of his life developing electrodynamics, and he did that without the help of quaternions. Aside: There is an even more elegant way to represent Maxwell's equations, which is with 4-vectors. That approach also wasn't available to Maxwell. To answer the question raised in the opening post, "Did Maxwell actually derive his equations using the methods we use today or some other methods?" He did it tediously, one scalar equation at a time. Most physics texts and journal articles written in the late 19th century and earlier are tedious to read because they didn't have the aid of higher mathematical structures.
Reference https://www.physicsforums.com/threads/history-of-vector-analysis.753307/
Reference https://www.physicsforums.com/threads/history-of-vector-analysis.753307/
Open Archive
Summaries
This paper traces the development of the divergence theorem in three dimensions from 1813 to 1901, in its Cartesian coordinate form (1813–1875) by George Green, Carl F. Gauss and M. V. Ostrogradskii and then in its vector form (1880–1901) by Oliver Heaviside and Josiah W. Gibbs.
Cettee´tude trace le de´veloppement du theóre`me de divergence en trois dimensions de 1813a`1901, dans sa frome carte´sienne (1813–1875) par George Green, Carl F. Gauss et Michel Ostrogradskii, et ensuite dans sa forme vectorielle (1880–1901) par Olivier Heaviside et Josiah W. Gibbs.
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