向量微積分 定義
Vector calculus or vector analysis is the use of calculus (limits, derivatives, and integrals) with two or more independent variables, or two or more dependent variables. This can be thought of as the calculus of three dimensional figures. Vector calculus is concerned with differentiation and integration of vector fields, primarily in 3-dimensional Euclidean space R3. The term vector calculus is sometimes used as a synonym for the broader subject of multivariable calculus, which includes vector calculus as well as partial differentiation and multiple integration. Common elements of multivariable calculus include parametric equations, vectors, partial derivatives, multiple integrals, line integrals, and surface integrals. Vector calculus plays an important role in differential geometry and in the study of partial differential equations. It is used extensively in physics and engineering, especially in the description of electromagnetic fields, gravitational fields and fluid flow.
概述
向量微積分是由 J. Willard Gibbs 和 Oliver Heaviside 在 19 世紀末期從四元數分析發展而來的,大部分符號和術語是由 Gibbs 和 Edwin Bidwell Wilson 在他們 1901 年的著作《向量分析》中建立的。在使用叉積的傳統形式中,向量微積分不能推廣到更高維度,而使用外積的幾何代數的替代方法確實可以推廣。
來源
“Vector Calculus.” Wikipedia, Wikimedia Foundation, 19 Apr. 2020, en.wikipedia.org/wiki/Vector_calculus.