Changes
Jump to navigation
Jump to search
Created the page
The '''Laplacian''' is an [[operator]] in vector calculus. It is denoted using a nabla, <math>\nabla^2</math> For some [[scalar]] function that takes in <math>n</math> variables, <math>f(x_1, x_2,x_3,... x_n)</math>, the Laplacian may be defined as:
<math>
\nabla^2 f
= \sum\limits_{i=1}^{n} \frac{\partial^2 f}{\partial x_i^2}
= \frac{\partial^2 f}{\partial x_1^2} + \frac{\partial^2 f}{\partial x_2^2} + ... + \frac{\partial^2 f}{\partial x_n^2}
</math>
In [[Cartesian coordinates]], the function is <math>f(x,y,z)</math>. The Laplacian is:
<math>
\nabla^2 f = \frac{\partial^2 f}{\partial x^2} + \frac{\partial^2 f}{\partial y^2} + \frac{\partial^2 f}{\partial z^2}
</math>
==See Also==
*[[Curl]]
*[[Divergence]]
*[[Gradient]]
[[Category:Mathematics]]
[[Category:Vector Analysis]]
<math>
\nabla^2 f
= \sum\limits_{i=1}^{n} \frac{\partial^2 f}{\partial x_i^2}
= \frac{\partial^2 f}{\partial x_1^2} + \frac{\partial^2 f}{\partial x_2^2} + ... + \frac{\partial^2 f}{\partial x_n^2}
</math>
In [[Cartesian coordinates]], the function is <math>f(x,y,z)</math>. The Laplacian is:
<math>
\nabla^2 f = \frac{\partial^2 f}{\partial x^2} + \frac{\partial^2 f}{\partial y^2} + \frac{\partial^2 f}{\partial z^2}
</math>
==See Also==
*[[Curl]]
*[[Divergence]]
*[[Gradient]]
[[Category:Mathematics]]
[[Category:Vector Analysis]]
(username removed)