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The notation $\nabla^2$ (nabla squared) is mathematically equivalent to $\Delta$ (delta) when representing the Laplacian operator. Both symbols denote the sum of the unmixed second partial derivatives of a scalar field.

Conditions: The operator acts on a scalar field $u$.; The context is vector calculus or PDEs.; $\nabla$ is the del/nabla operator.; $\Delta$ is the Laplace operator.

The notation $\nabla^2$ (nabla squared) is mathematically equivalent to $\Delta$ (delta) when representing the Laplacian operator. Both symbols denote the sum of the unmixed second partial derivatives of a scalar field.

Conditions: The operator acts on a scalar field $u$.; The context is vector calculus or PDEs.; $\nabla$ is the del/nabla operator.; $\Delta$ is the Laplace operator.

The upside-down triangle symbol, known as nabla ($\nabla$), represents the del operator. In the context of Laplace's equation, its square ($\nabla^2$) is equivalent to the Laplacian operator ($\Delta$).

Conditions: The symbol $\nabla$ is the vector differential operator.; $\nabla^2$ denotes the composition of the divergence of the gradient, resulting in a scalar operator.; The equation is the Laplace equation.

The upside-down triangle symbol, known as nabla ($\nabla$), represents the del operator. In the context of Laplace's equation, its square ($\nabla^2$) is equivalent to the Laplacian operator ($\Delta$).

Conditions: The symbol $\nabla$ is the vector differential operator.; $\nabla^2$ denotes the composition of the divergence of the gradient, resulting in a scalar operator.; The equation is the Laplace equation.