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==Applications: Harmonic Functions==
 
==Applications: Harmonic Functions==
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==Definition==
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Harmonic functions are functions that satisfy the equation
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<math>
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\frac{\partial^{2} f}{\partial x_{1}^{2}}+\frac{\partial^{2} f}{\partial x_{2}^{2}}+\cdots+\frac{\partial^{2} f}{\partial x_{n}^{2}}=0
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</math>
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or <math> \large\Delta f = div(\nabla f) = \nabla\cdot\nabla f = \nabla^{2} f = 0 </math>.
  
 
[[Walther_MA271_Fall2020_topic9|Back to main page]]
 
[[Walther_MA271_Fall2020_topic9|Back to main page]]

Revision as of 16:37, 6 December 2020


Applications: Harmonic Functions

Definition

Harmonic functions are functions that satisfy the equation

$ \frac{\partial^{2} f}{\partial x_{1}^{2}}+\frac{\partial^{2} f}{\partial x_{2}^{2}}+\cdots+\frac{\partial^{2} f}{\partial x_{n}^{2}}=0 $

or $ \large\Delta f = div(\nabla f) = \nabla\cdot\nabla f = \nabla^{2} f = 0 $.

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Alumni Liaison

Ph.D. 2007, working on developing cool imaging technologies for digital cameras, camera phones, and video surveillance cameras.

Buyue Zhang