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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.