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Mathematics

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Mathematical Analysis

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Calculus

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Multivariable/Multi-Variable/Multivariate Calculus/Analysis

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Laplacian Operator (𝛻·𝛻 | 𝛻·𝛻𝑓 | 𝛻² | 𝛻²𝑓 | 𝛥 | 𝛥𝑓)

Harmonic Functions

Created on Dec 19, 2023

Harmonic Functions
  • is a scalar-valued function 𝑓(𝑥1, …, 𝑥𝑛) whose Laplacian is equal to zero:
    • 𝛥f=∑in​dxi2​d2f​=0
  • intuitively, given 𝑓 and a point 𝑥; the average of all points within a distance/radius from 𝑥 is also 𝑥

Resources

  • https://www.khanacademy.org/math/multivariable-calculus/multivariable-derivatives/laplacian/v/harmonic-functions