can be thought of as an extension of the second-order derivative 𝑑²𝑓/𝑑𝑥² but for a scalar-valued function
is defined as the divergence (𝛻·) of the gradient (𝛻𝑓)
if 𝑓 is a twice-differentiable scalar-valued function, then the Laplacian of 𝑓 is a scalar-valued function defined by:
- $𝛥 f = \nabla^{2} f = \nabla \cdot \nabla f$
explicitly, the Laplacian of 𝑓 is the sum of all the unmixed second partial derivatives in the Cartesian coordinates 𝑥_𝑖:
- $𝛥 f = \sum_{i = 1}^{n} \frac{𝜕 ^{2} f}{𝜕 x _{i}^{2}}$

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