Difference between revisions of "Laplacian"
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| − | 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: | + | 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:<ref>[http://mathworld.wolfram.com/Laplacian.html Laplacian] from Wolfram MathWorld</ref> |
<math> | <math> | ||
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\nabla^2 f = \frac{\partial^2 f}{\partial x^2} + \frac{\partial^2 f}{\partial y^2} + \frac{\partial^2 f}{\partial z^2} | \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> | </math> | ||
| + | |||
| + | ==References== | ||
| + | {{reflist}} | ||
==See also== | ==See also== | ||
Latest revision as of 16:27, September 11, 2017
The Laplacian is an operator in vector calculus. It is denoted using a nabla, For some scalar function that takes in variables, , the Laplacian may be defined as:[1]
In Cartesian coordinates, the function is . The Laplacian is:
