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Vector calculus or vector analysis is a branch of mathematics concerned with the differentiation and integration of vector fields, primarily in three-dimensional Euclidean space, . [1] The term vector calculus is sometimes used as a synonym for the broader subject of multivariable calculus, which spans vector calculus as well as partial differentiation and multiple integration.
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 ...
La matematica da scienza delle grandezze a teoria delle forme: l ' Ausdehnungslehre di H. Grassmann [The Mathematics of Quantities to the Science of Forms: The Ausdehnungslehre of H. Grassmann] (PDF) (PhD thesis) (in Italian). University of Genoa. Crowe, Michael J. (1967). A History of Vector Analysis. University of Notre Dame Press. ISBN 0-486 ...
:Used concepts developed in the then-current textbooks (e.g., vector analysis and non-Euclidean geometry) to provide entry into mathematical physics with a vector-based introduction to quaternions and a primer on matrix notation for linear transformations of 4-vectors. The ten chapters are composed of 4 on kinematics, 3 on quaternion methods ...
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.As a scholarly treatment of a reformation in technical communication, the text is a contribution to the history of science.
He is best known for writing the influential book A History of Vector Analysis. [2] After the Great Vector Debate of the 1890s it was generally assumed that quaternions had been superseded by vector analysis. But in his book, published in 1967, Crowe showed how, contrarily, vector analysis directly stemmed from the quaternions. [3]
Another method of deriving vector and tensor derivative identities is to replace all occurrences of a vector in an algebraic identity by the del operator, provided that no variable occurs both inside and outside the scope of an operator or both inside the scope of one operator in a term and outside the scope of another operator in the same term ...
Vector Analysis, a textbook on vector calculus by Wilson, first published in 1901, which did much to standardize the notation and vocabulary of three-dimensional linear algebra and vector calculus; Vector bundle, a topological construction that makes precise the idea of a family of vector spaces parameterized by another space