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<math> | <math> | ||
\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 | \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 | ||
| − | </math> | + | </math>, or <math> \large\Delta f = \nabla^{2} f = 0 </math>. |
| − | + | ||
| − | or <math> \large\Delta 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 15:37, 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 = \nabla^{2} f = 0 $.
