Vector Analysis
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 20th 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
Professor Gibbs used an 85 page outline of his vector system at Yale; he sent a copy to Oliver Heaviside in 1888. Accordingly, in 1892 when Heaviside was describing his own vector system in the Transactions of the Royal Society, Heaviside praised Gibbs' "little book", saying it "deserves to be well known". However, he also notes 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 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 Mills Peirce 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 über 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.
- Oliver Heaviside (1892) "On the forces, stresses, and fluxes of energy in the electromagnetic field", Philosophical Transactions of the Royal Society of London A 183:423–80.
- Edwin Bidwell Wilson (1931)"Reminiscences of Gibbs by a student and colleague" Bulletin of the American Mathematical Society. Volume 37, Number 6, 401–416.