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Laplacian of scalar function

`laplacian(f,x)`

`laplacian(f)`

Compute the Laplacian of this symbolic expression. By default,
`laplacian`

computes the Laplacian of an expression with respect to a
vector of all variables found in that expression. The order of variables is defined by
`symvar`

.

syms x y t laplacian(1/x^3 + y^2 - log(t))

ans = 1/t^2 + 12/x^5 + 2

Create this symbolic function:

syms x y z f(x, y, z) = 1/x + y^2 + z^3;

Compute the Laplacian of this function with respect to the vector ```
[x, y,
z]
```

:

L = laplacian(f, [x y z])

L(x, y, z) = 6*z + 2/x^3 + 2

If

`x`

is a scalar,`laplacian(f, x) = diff(f, 2, x)`

.

The Laplacian of a scalar function or functional expression is the divergence of the gradient of that function or expression:

$$\Delta f=\nabla \cdot \left(\nabla f\right)$$

Therefore, you can compute the Laplacian using the `divergence`

and `gradient`

functions:

```
syms f(x, y)
divergence(gradient(f(x, y)), [x y])
```

`curl`

| `diff`

| `divergence`

| `gradient`

| `hessian`

| `jacobian`

| `potential`

| `vectorPotential`