Vector Analysis (Gibbs/Wilson)

Vector Analysis (Gibbs/Wilson)

"Vector Analysis" is a book on vector calculus first published in 1901 by Edwin Bidwell Wilson. Its subtitle is "A Text-book for the use of students of mathematics and physics, founded upon the lectures of J. Willard Gibbs Ph.D. LL.D." This textbook did much to standardize vocabulary and notations for description of three-dimensional linear algebra in the twentieth century. It was reprinted in 1913, 1916, 22, 25, 29, 31, and 1943. In 1960 Dover Publications began to print and distribute this enduring textbook. It is now available on-line (see link below).

Contents

The first chapter covers 3-dimensional vectors in space, the concept of a (real) scalar, and the product of a scalar with a vector.

The second chapter introduces the dot product of two vectors and the cross product as well. These are extended to a scalar triple product and a quadruple product. Then in pages 77–81 one finds the essentials of spherical trigonometry, a topic of considerable value at the time due to its connection with celestial navigation.

The third chapter begins the vector calculus with the introduction of the del operator.

Genesis

On the occasion of the bicentennial of Yale University, a series of publications were issued to underscore the important role of Yale in the advancement of knowledge. Gibbs was authoring "Elementary Principles in Statistical Mechanics" for the series. Mindful of the collegiate demand for innovative textbooks, the editor of the series, Professor Morris, sought to include a book-length treatment of the pamphlet on vectors that Gibbs used with students. But the professor had enough writing to do for "Statistical Mechanics". The natural solution at a university is to enlist the services of a graduate student. One incoming graduate from Harvard was E. B. Wilson. It fell to Dean A.W. Phillips at Yale to persuade Wilson to take the Gibbs vector course. (Wilson already knew the material from his course on quaternions with James Mill Pierce at Harvard.) Once the course was completed, and Gibbs had gotten to know Wilson, then Morris approached Wilson for the project. Thus Wilson became the “author” of the book by expanding his class notes, providing exercises, and coordinating with other consultants, including his father.

References

* Alexander Ziwet (review) "Bulletin of the American Mathematical Association" 8:207–15.
* Anon. (review) "Bulletin des sciences mathematique" 26:21–30.
* Victor Schlegel (review) "Jahrbuch uber die Fortschritte der Mathematik" 33:96–7.
* Cargill Gilston Knott (review) Philosophical Magazine" 6th Ser, 4:614–22.
* Crowe, M.J. (1967) A History of Vector Analysis, Notre Dame University Press.
* [http://projecteuclid.org/euclid.bams/1183494779 Wilson E.B. (1931), "Reminiscences of Gibbs by a student and colleague", "Bulletin of the American Mathematical Society." Volume 37, Number 6, 401–416.]

External links

[http://www.archive.org/details/117714283 A free online version of the book]


Wikimedia Foundation. 2010.

Игры ⚽ Нужно решить контрольную?

Look at other dictionaries:

  • 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… …   Wikipedia

  • Josiah Willard Gibbs — Infobox Scientist box width = 300px name = J. Willard Gibbs image size = 300px caption = Josiah Willard Gibbs birth date = birth date|1839|2|11|mf=y birth place = New Haven, Connecticut, USA death date = death date and… …   Wikipedia

  • Vector calculus — Topics in Calculus Fundamental theorem Limits of functions Continuity Mean value theorem Differential calculus  Derivative Change of variables Implicit differentiation Taylor s theorem Related rates …   Wikipedia

  • Laplace–Runge–Lenz vector — Throughout this article, vectors and their magnitudes are indicated by boldface and italic type, respectively; for example, left| mathbf{A} ight| = A. In classical mechanics, the Laplace–Runge–Lenz vector (or simply the LRL vector) is a vector… …   Wikipedia

  • Edwin Bidwell Wilson — (April 25 1879 – December 28 1964) was a mathematician and polymath. He was the sole protegé of Yale s physicist Josiah Willard Gibbs and was mentor to Harvard economist Paul Samuelson. [ [http://nobelprize.org/nobel… …   Wikipedia

  • History of quaternions — This article is an indepth story of the history of quaternions. It tells the story of who and when. To find out what quaternions are see quaternions and to learn about historical quaternion notation of the 19th century see classical quaternions… …   Wikipedia

  • Hyperbolic quaternion — In mathematics, a hyperbolic quaternion is a mathematical concept first suggested by Alexander MacFarlane in 1891 in a speech to the American Association for the Advancement of Science. The idea was criticized for its failure to conform to… …   Wikipedia

  • Quaternion — Quaternions, in mathematics, are a non commutative extension of complex numbers. They were first described by the Irish mathematician Sir William Rowan Hamilton in 1843 and applied to mechanics in three dimensional space. They find uses in both… …   Wikipedia

  • List of important publications in physics — Optics Book of Optics *Ibn al Haytham (Alhacen)Description: The Book of Optics (Arabic: Kitab al Manazir , Latin: De Aspectibus ) is a seven volume treatise on optics and physics, written by the Iraqi Arab Muslim scientist Ibn al Haytham… …   Wikipedia

  • List of mathematics articles (V) — NOTOC Vac Vacuous truth Vague topology Valence of average numbers Valentin Vornicu Validity (statistics) Valuation (algebra) Valuation (logic) Valuation (mathematics) Valuation (measure theory) Valuation of options Valuation ring Valuative… …   Wikipedia

Share the article and excerpts

Direct link
… Do a right-click on the link above
and select “Copy Link”