Method on @sym: laplacian (f) ¶

Method on @sym: laplacian (f, x) ¶

Symbolic Laplacian of symbolic expression.

The Laplacian of a scalar expression f is the scalar expression:

syms f(x, y, z)
laplacian(f)
  ⇒ (sym)
        2                 2                 2
       ∂                 ∂                 ∂
      ───(f(x, y, z)) + ───(f(x, y, z)) + ───(f(x, y, z))
        2                 2                 2
      ∂x                ∂y                ∂z

x can be a scalar, vector or cell list. If omitted, it is determined using symvar.

Example:

syms x y
laplacian(x^3 + 5*y^2)
  ⇒ (sym) 6⋅x + 10

Note: assumes x is a Cartesian coordinate system.

See also: @@sym/divergence, @@sym/gradient, @@sym/curl, @@sym/jacobian, @@sym/hessian.

Package: symbolic