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.