Multivariable calculus

Level set

In mathematics, a level set of a real-valued function f of n real variables is a set where the function takes on a given constant value c, that is: When the number of independent variables is two, a level set is called a level curve, also known as contour line or isoline; so a level curve is the set of all real-valued solutions of an equation in two variables x1 and x2. When n = 3, a level set is called a level surface (or isosurface); so a level surface is the set of all real-valued roots of an equation in three variables x1, x2 and x3. For higher values of n, the level set is a level hypersurface, the set of all real-valued roots of an equation in n > 3 variables. A level set is a special case of a fiber. (Wikipedia).

Level set
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Metric space | Level-set method | Mathematical optimization | Gradient | Theorem | Differentiable function | Singular point of an algebraic variety | Function of several real variables | Surface (mathematics) | Contour line | Curve | Level set (data structures) | Quasiconvex function | Extreme value theorem | Hypersurface | Empty set | Isosurface | Epigraph (mathematics) | Intersection theory | Himmelblau's function | Mathematics | Set (mathematics) | Cusp (singularity) | Sphere | Critical point (mathematics) | Manifold | Fiber (mathematics) | Indifference curve | Real-valued function | Constant (mathematics) | Circle | Convex set | Implicit curve