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:

GO FURTHER

Multivariable Calculus Web App

RELATED EXAMPLES

  • Derivatives
  • Integrals
  • Integral Transforms
  • Limits
  • Matrices
  • Vectors
  • Jacobian

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

    Compute a Jacobian determinant:

    Compute a Jacobian matrix: