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

### Jacobian

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