Non-deterministic, or stochastic, systems can be studied using a different kind of mathematics, such as stochastic calculus. Multivariable calculus is used in many fields of natural and social science and engineering to model and study high-dimensional systems that exhibit deterministic behavior. Extensions of concepts used for single variable functions may require caution. Functions with independent variables corresponding to each of the degrees of freedom are often used to model these systems, and multivariable calculus provides tools for characterizing the system dynamics.Ī Scalar Field: A scalar field shown as a function of (x,y). Multivariable calculus can be applied to analyze deterministic systems that have multiple degrees of freedom. Multivariable calculus (also known as multivariate calculus) is the extension of calculus in one variable to calculus in more than one variable: the differentiated and integrated functions involve multiple variables, rather than just one. divergence: a vector operator that measures the magnitude of a vector field’s source or sink at a given point, in terms of a signed scalar. deterministic: having exactly predictable time evolution.In multivariable calculus, gradient, Stokes’, divergence, and Green theorems are specific incarnations of a more general theorem: the generalized Stokes’ theorem.Unlike a single variable function f(x), for which the limits and continuity of the function need to be checked as x varies on a line (x-axis), multivariable functions have infinite number of paths approaching a single point.Multivariable calculus can be applied to analyze deterministic systems that have multiple degrees of freedom.
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December 2022
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