Level Set
المؤلف:
Gray, A
المصدر:
"Level Surfaces in R^3." §12.7 in Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press
الجزء والصفحة:
pp. 291-293
30-9-2021
1683
Level Set
The level set of a differentiable function 
corresponding to a real value 
is the set of points
![<span style=]() {(x_1,...,x_n) in R^n:f(x_1,...,x_n)=c}. " src="https://mathworld.wolfram.com/images/equations/LevelSet/NumberedEquation1.gif" style="height:15px; width:218px" /> |
For example, the level set of the function 
corresponding to the value 
is the sphere 
with center 
and radius 
.
If 
, the level set is a plane curve known as a level curve. If 
, the level set is a surface known as a level surface.
REFERENCES:
Gray, A. "Level Surfaces in 
." §12.7 in Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, pp. 291-293, 1997.
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