Vector Analysis

Vector Analysis is a textbook by Edwin Bidwell Wilson, first published in 1901¹ and based on the lectures that Josiah Willard Gibbs had delivered on the subject at Yale University. The book did much to standardize the notation and vocabulary of three-dimensional linear algebra and vector calculus, as used by physicists and mathematicians. It was reprinted by Yale in 1913, 1916, 1922, 1925, 1929, 1931, and 1943. The work is now in the public domain. It was reprinted by Dover Publications in 1960.

Vector Analysis is a textbook by Edwin Bidwell Wilson, first published in 1901 and based on the lectures that Josiah Willard Gibbs had delivered on the subject at Yale University. The book did much to standardize the notation and vocabulary of three-dimensional linear algebra and vector calculus, as used by physicists and mathematicians. It was reprinted by Yale in 1913, 1916, 1922, 1925, 1929, 1931, and 1943. The work is now in the public domain. It was reprinted by Dover Publications in 1960. ==Genesis== Hermann Grassmann had introduced basic ideas of a linear space in 1844 and 1862, and W. K. Clifford published Elements of Dynamic in 1878¹, so as Gibbs was teaching physics in the 1880s he took these developments into consideration for his students. A pamphlet that he printed for them acknowledges both Grassmann and Clifford. The influence of Grassmann is seen in the bivectors, and the influence of Clifford in the decomposition of the quaternion product into scalar product and cross product. In 1888 Gibbs sent a copy of his pamphlet to Oliver Heaviside who was formulating his own vectorial system in the Transactions of the Royal Society, praised Gibbs' "little book", saying it "deserves to be well known". However, he also noted that it was "much too condensed for a first introduction to the subject". On the occasion of the bicentennial of Yale University, a series of publications were to be issued to showcase Yale's role in the advancement of knowledge. Gibbs was authoring Elementary Principles in Statistical Mechanics for that series. Mindful of the demand for innovative university textbooks, the editor of the series, Professor Morris, wished to include also a volume dedicated to Gibbs's lectures on vectors, but Gibbs's time and attention were entirely absorbed by the Statistical Mechanics. E. B. Wilson was then a new graduate student in mathematics. He had learned about quaternions from James Mills Peirce at Harvard, but Dean A. W. Phillips persuaded him to take Gibbs's course on vectors, which treated similar problems from a rather different perspective. After Wilson had completed the course, Morris approached him about the project of producing a textbook. Wilson wrote the book by expanding his own class notes, providing exercises, and consulting with others (including his father). File:Wilson-1.jpg|1907 copy of Vector Analysis File:Wilson-3.jpg|Preface to Vector Analysis (1907) File:Wilson-4.jpg|Table of contents to Vector Analysis (1907) File:Wilson-5.jpg|First page of Vector Analysis (1907) ==References== ==Further reading== Alexander Ziwet (1902) Review of Vector Analysis, Bulletin of the American Mathematical Society 8:207–15. Anon. (review) Bulletin des sciences mathématiques 26:21–30. Victor Schlegel (review) Jahrbuch über die Fortschritte der Mathematik 33:96–7. Cargill Gilston Knott (review) Philosophical Magazine 6th Ser, 4:614–22. Michael J. Crowe (1967) A History of Vector Analysis, Notre Dame University Press. ==External links== E. B. Wilson (1901) Vector Analysis, based on the Lectures of J. W. Gibbs at Internet Archive.

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