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... 17 KB (2,201 words) - 15:54, 31 October 2023 |
In multivariable calculus, the implicit function theorem is a tool that allows relations to be converted to functions of several real variables. It does... 23 KB (3,816 words) - 20:19, 12 May 2024 |
fewer functions than untyped lambda calculus. List of types of functions List of functions Function fitting Implicit function Higher-order function Homomorphism... 75 KB (11,220 words) - 17:58, 11 May 2024 |
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... 37 KB (6,894 words) - 05:50, 7 April 2024 |
vectors and column vectors of multivariable functions, see matrix calculus. A real-valued implicit function of several real variables is not written in... 47 KB (7,458 words) - 15:36, 11 January 2024 |
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... 21 KB (3,560 words) - 17:09, 16 April 2024 |
(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... 31 KB (4,447 words) - 09:20, 21 April 2024 |
Critical point (mathematics) (category Smooth functions) 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... 20 KB (2,979 words) - 09:19, 10 May 2024 |
Look up implicit in Wiktionary, the free dictionary. Implicit may refer to: Implicit function Implicit function theorem Implicit curve Implicit surface... 805 bytes (116 words) - 04:22, 10 February 2021 |
aspect of the proof is an implicit function theorem for isometric embeddings. The usual formulations of the implicit function theorem are inapplicable... 69 KB (7,378 words) - 00:08, 7 May 2024 |
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... 9 KB (1,584 words) - 21:33, 28 January 2023 |
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... 12 KB (1,944 words) - 10:25, 28 February 2024 |
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... 16 KB (1,893 words) - 13:05, 10 March 2024 |
Surface (mathematics) (section Implicit surface) a continuous function of two variables. The set of the zeros of a function of three variables is a surface, which is called an implicit surface. If the... 22 KB (3,923 words) - 03:17, 4 February 2024 |
{\displaystyle x^{2}+y^{2}-1=0} . An implicit function is a function that is defined implicitly by an implicit equation, by associating one of the variables... 88 KB (10,913 words) - 11:59, 19 April 2024 |
Nash–Moser theorem (redirect from Nash-Moser inverse function theorem) smooth functions. It is particularly useful when the inverse to the derivative "loses" derivatives, and therefore the Banach space implicit function theorem... 22 KB (3,536 words) - 22:08, 27 March 2024 |
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... 16 KB (2,240 words) - 22:28, 20 March 2024 |
Nash functions are those functions needed in order to have an implicit function theorem in real algebraic geometry. Along with Nash functions one defines... 5 KB (714 words) - 22:30, 12 March 2024 |
{\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... 9 KB (1,299 words) - 20:21, 16 April 2024 |
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 ... 27 KB (6,234 words) - 06:43, 8 February 2024 |
differentiation. A more recent work along this direction uses the implicit function theorem to calculate hypergradients and proposes a stable approximation... 23 KB (2,460 words) - 16:35, 4 January 2024 |
Manifold (section Scalar-valued functions) continuously differentiable function between Euclidean spaces that satisfies the nondegeneracy hypothesis of the implicit function theorem. In the third section... 67 KB (9,476 words) - 21:20, 15 February 2024 |
{\displaystyle f(x,y,z)>1} . Therefore, the implicit function is also called the inside-outside function of the superellipsoid. The superellipsoid has... 16 KB (2,307 words) - 13:28, 27 February 2024 |
differential topology, the preimage theorem is a variation of the implicit function theorem concerning the preimage of particular points in a manifold... 3 KB (454 words) - 22:27, 22 June 2022 |
Curvature (section Implicit curve) from the expression of the curvature of the graph of a function by using the implicit function theorem and the fact that, on such a curve, one has d y... 44 KB (6,425 words) - 07:31, 10 May 2024 |