| Line 2: | Line 2: | ||
==Applications: Harmonic Functions== | ==Applications: Harmonic Functions== | ||
| + | |||
| + | ==Definition== | ||
| + | |||
| + | Harmonic functions are functions that satisfy the equation | ||
| + | |||
| + | <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 | ||
| + | </math> | ||
| + | |||
| + | 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 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 = div(\nabla f) = \nabla\cdot\nabla f = \nabla^{2} f = 0 $.
