Various important formulas for vector calculus are given below: For a particular surface, a scalar field or a vector field can be integrated over a surface. It means that the double integral is related to the line integral. Read More: Differentiation and Integration FormulaĪ surface integral is an abstraction of various integrals to the integrations over surfaces. Sometimes, a line integral can also be called a curve integral, curvilinear integral or path integral. ![]() For example, one can also integrate a scalar-valued function along a curve. The integration can be done with some specific type of functions with vector value along with a curve. In other words, it can be defined as an integral in which the function is calculated along with a curve when it is about to be integrated. Vector calculus is also shown to work in two different forms of integrals known as the line integrals and the surface integrals.Ī line integral of a vector field is some function’s integral along a curve. Vector analysis is the kind of analysis where we deal with quantities having both the magnitude and the direction. In the Euclidean space, a domain’s vector field is shown as a vector-valued function that does the comparison of the real number’s n-tuple to each point on the domain. Vector fields show the distribution of a particular vector to each point in the space’s subset. ![]() It deals with the integration and the differentiation of the vector field in the Euclidean Space of three dimensions. Vector calculus can also be called vector analysis.
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