向量微积分 定义
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
向量微积分是由 J. Willard Gibbs 和 Oliver Heaviside 在 19 世纪末期从四元数分析发展而来的,大部分符号和术语是由 Gibbs 和 Edwin Bidwell Wilson 在他们 1901 年的著作《向量分析》中建立的。在使用叉积的传统形式中,向量微积分不能推广到更高维度,而使用外积的几何代数的替代方法确实可以推广。
来源
“Vector Calculus.” Wikipedia, Wikimedia Foundation, 19 Apr. 2020, en.wikipedia.org/wiki/Vector_calculus.