# Multivariate calculus

**Multivariate calculus**is a means of analyzing deterministic systems with multiple degrees of freedom. Functions with independent variables corresponding to each of the degrees of freedom are often used to model these systems, and the calculus provides tools for characterizing the system dynamics.

Typical operations in multivariate calculus are partial differentiation and integration over areas or volumes. The differentiation operation formulates the rate of change of the system behavior with respect to one or more of the degrees of freedom. Inversely, integration averages the system behavior across the span of one or more of its constituent variables.

Multivariate calculus is used in many fields of natural and social science and engineering to model and study high-dimensional systems that exhibit deterministic behavior. Non-deterministic, or stochastic systems, are better modeled using regression or other statistical methods.

*See also*: list of multivariable calculus topics, multivariate statistics