Examples for

Vector analysis is the study of calculus over vector fields. Operators such as divergence, gradient and curl can be used to analyze the behavior of scalar- and vector-valued multivariate functions. Wolfram|Alpha can compute these operators along with others, such as the Laplacian, Jacobian and Hessian.

Find the gradient of a multivariable function in various coordinate systems.

Calculate the curl of a vector field.

Calculate the Hessian matrix and determinant of a multivariate function.

Calculate the divergence of a vector field.

Find the Laplacian of a function in various coordinate systems.

Explore identities involving vector functions and operators, such as div, grad and curl.

Multivariable Calculus Web App

Calculate the Jacobian matrix or determinant of a vector-valued function.