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In single-variable calculus, the fundamental theorem of calculus establishes a link between the derivative and the integral. The link between the derivative and the integral in multivariable calculus is embodied by the integral theorems of vector calculus: [1]: 543ff Gradient theorem; Stokes' theorem; Divergence theorem; Green's theorem.
Some suggest that multivariate regression is distinct from multivariable regression, however, that is debated and not consistently true across scientific fields. [2] Principal components analysis (PCA) creates a new set of orthogonal variables that contain the same information as the original set. It rotates the axes of variation to give a new ...
The second Cousin problem starts with a similar set-up to the first, specifying instead that each ratio / is a non-vanishing holomorphic function (where said difference is defined). It asks for a meromorphic function f {\displaystyle f} on M such that f / f i {\displaystyle f/f_{i}} is holomorphic and non-vanishing.
When f is a differentiable function between manifolds, the inverse function theorem gives conditions for this to be single-valued locally in X. For example, the complex logarithm log(z) is the multivalued inverse of the exponential function e z : C → C ×, with graph
In probability, and statistics, a multivariate random variable or random vector is a list or vector of mathematical variables each of whose value is unknown, either because the value has not yet occurred or because there is imperfect knowledge of its value.
The common usage, much older than the general definition of functions between sets, is to not use double parentheses and to simply write f(x 1, x 2, …, x n). It is also common to abbreviate the n-tuple (x 1, x 2, …, x n) by using a notation similar to that for vectors, like boldface x, underline x, or overarrow x →. This article will use ...
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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.