mathematics, an implicit equation is a relation of the form R ( x 1 , … , x n ) = 0 , {\displaystyle R(x_{1},\dots ,x_{n})=0,} where R is a function of several...

In multivariable calculus, the implicit function theorem is a tool that allows relations to be converted to functions of several real variables. It does...

fewer functions than untyped lambda calculus. History of the function concept List of types of functions List of functions Function fitting Implicit function...

proof is quite similar to the proof of the implicit function theorem and, in fact, the implicit function theorem can be also used instead.) More generally...

set of zeros of a function of three variables. Implicit means that the equation is not solved for x or y or z. The graph of a function is usually described...

using theorem differentiation under the integral sign. A real-valued implicit function of a real variable is not written in the form "y = f(x)". Instead...

(These two functions also happen to meet (−1, 0) and (1, 0), but this is not guaranteed by the implicit function theorem.) The implicit function theorem...

vectors and column vectors of multivariable functions, see matrix calculus. A real-valued implicit function of several real variables is not written in...

for some function F of two variables. Hence an implicit curve can be considered as the set of zeros of a function of two variables. Implicit means that...

aspect of the proof is an implicit function theorem for isometric embeddings. The usual formulations of the implicit function theorem are inapplicable...

Look up implicit in Wiktionary, the free dictionary. Implicit may refer to: Implicit function Implicit function theorem Implicit curve Implicit surface...

generalization includes generalizations of the inverse function theorem and the implicit function theorem, where the non-nullity of the derivative is replaced...

y-axis, and that, at this point, g does not define an implicit function from x to y (see implicit function theorem). If (x0, y0) is such a critical point, then...

{\displaystyle z=a} . This is the case for functions defined by the implicit function theorem or by a Taylor series around z = a {\displaystyle z=a} . In...

Amazigo, John C.; Rubenfeld, Lester A. (1980). "Implicit Functions; Jacobians; Inverse Functions". Advanced Calculus and its Applications to the Engineering...

three variables can be related by a function of the form f(x, y, z) = 0, so each variable is given as an implicit function of the other two variables. For...

Ck- case was later extrapolated into the h-principle and Nash–Moser implicit function theorem. A simpler proof of the second Nash embedding theorem was...

field V. The implicit function f is found by integrating the vector field V. Since not every vector field is the gradient of a function, the problem may...

the theory of real functions was also important in the development of the concept of the measure on a set. The implicit function theorem is known in...

smooth functions. It is particularly useful when the inverse to the derivative "loses" derivatives, and therefore the Banach space implicit function theorem...

differential topology, the preimage theorem is a variation of the implicit function theorem concerning the preimage of particular points in a manifold...

the function implicitly defined by f ( x ) 5 + f ( x ) + x = 0 {\displaystyle f(x)^{5}+f(x)+x=0} . In more precise terms, an algebraic function of degree...

principle, inverse function theorem, and implicit function theorems also hold. For a generalized version of the implicit function theorem to complex variables...

The implicit-association test (IAT) is an assessment intended to detect subconscious associations between mental representations of objects (concepts)...

isometrically embedded as well. Such a result is highly reminiscent of an implicit function theorem, and many authors have attempted to put the logic of the proof...

derivatives of functions Implicit function theorem – On converting relations to functions of several real variables Integration of inverse functions – Mathematical...

understood as an informational processing system with explicit and implicit functioning that is made up of a sensory processor, short-term (or working) memory...

we shall use the Implicit function theorem (Statement of the theorem ); we notice that for a continuously differentiable function f : R n + m → R m ...

{\displaystyle f(x,y,z)>1} . Therefore, the implicit function is also called the inside-outside function of the superellipsoid. The superellipsoid has...

mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of...