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.
Compute the gradient of a function:
Compute the gradient of a function specified in polar coordinates:
Calculate the curl of a vector field.
Compute the curl (rotor) of a vector field:
Calculate the Hessian matrix and determinant of a multivariate function.
Compute a Hessian determinant:
Compute a Hessian matrix:
Calculate the divergence of a vector field.
Compute the divergence of a vector field:
Find the Laplacian of a function in various coordinate systems.
Compute the Laplacian of a function:
Explore identities involving vector functions and operators, such as div, grad and curl.
Calculate alternate forms of a vector analysis expression:
GO FURTHERMultivariable Calculus Web App
Calculate the Jacobian matrix or determinant of a vector-valued function.