Examples for
Vector Analysis
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.
Gradient
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:
Curl
Calculate the curl of a vector field.
Compute the curl (rotor) of a vector field:
Hessian
Calculate the Hessian matrix and determinant of a multivariate function.
Compute a Hessian determinant:
Compute a Hessian matrix:
Divergence
Calculate the divergence of a vector field.
Compute the divergence of a vector field:
Laplacian
Find the Laplacian of a function in various coordinate systems.
Compute the Laplacian of a function:
Vector Analysis Identities
Explore identities involving vector functions and operators, such as div, grad and curl.
Calculate alternate forms of a vector analysis expression:
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Multivariable Calculus Web AppRELATED EXAMPLES
Jacobian
Calculate the Jacobian matrix or determinant of a vector-valued function.