In mathematics, the inverse function theorem is a theorem that asserts that, if a real function f has a continuous derivative near a point where its derivative...

implicit function theorem. Inverse function theorem Constant rank theorem: Both the implicit function theorem and the inverse function theorem can be seen...

mathematics, the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f. The inverse of f exists if...

calculus, the inverse function rule is a formula that expresses the derivative of the inverse of a bijective and differentiable function f in terms of...

inversion theorem, also known as the Lagrange–Bürmann formula, gives the Taylor series expansion of the inverse function of an analytic function. Lagrange...

mathematics, the inverse trigonometric functions (occasionally also called antitrigonometric, cyclometric, or arcus functions) are the inverse functions of the...

Nash–Moser theorem, discovered by mathematician John Forbes Nash and named for him and Jürgen Moser, is a generalization of the inverse function theorem on Banach...

In mathematics, inverse mapping theorem may refer to: the inverse function theorem on the existence of local inverses for functions with non-singular...

of as inverses of each other. The first part of the theorem, the first fundamental theorem of calculus, states that for a continuous function f , an...

the inverse function f − 1 : I 2 → I 1 {\displaystyle f^{-1}:I_{2}\to I_{1}} are continuous, they have antiderivatives by the fundamental theorem of calculus...

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

fixed-point theorem is a fixed-point theorem in topology, named after L. E. J. (Bertus) Brouwer. It states that for any continuous function f {\displaystyle...

theorem describes the behaviour of holomorphic functions defined on the unit disk. It gives a lower bound on the size of a disk in which an inverse to...

mathematics, the Fourier inversion theorem says that for many types of functions it is possible to recover a function from its Fourier transform. Intuitively...

and have a continuous inverse. This is guaranteed to hold if φ is continuously differentiable by the inverse function theorem. Alternatively, the requirement...

integration Cavalieri's quadrature formula Fundamental theorem of calculus Integration by parts Inverse chain rule method Integration by substitution Tangent...

and Θ {\textstyle \Theta } is the parameter space. Using the inverse function theorem, it can be shown that s n − 1 {\textstyle s_{n}^{-1}} is well-defined...

a subset of X × Y. When f is a differentiable function between manifolds, the inverse function theorem gives conditions for this to be single-valued locally...

implicit function is an inverse function. Not all functions have a unique inverse function. If g is a function of x that has a unique inverse, then the...

exponential function is the inverse function of the natural logarithm. The inverse function theorem implies that the natural logarithm has an inverse function, that...

complex analytic topology. They satisfy the hypotheses of the implicit function theorem, but because open sets in the Zariski topology are so large, they are...

In calculus, Rolle's theorem or Rolle's lemma essentially states that any real-valued differentiable function that attains equal values at two distinct...

In vector calculus, Green's theorem relates a line integral around a simple closed curve C to a double integral over the plane region D (surface in R...

Matsumura 1989, Theorem 2.4 Griffiths & Harris 1994, p. 681 Eisenbud 1995, Corollary 19.5 McKernan, James. "The Inverse Function Theorem" (PDF). Archived...

fixed-point theorem is also applied in proving the existence of solutions of ordinary differential equations, and is used in one proof of the inverse function theorem...

has an inverse function, that inverse is continuous, and if a continuous map g has an inverse, that inverse is open. Given a bijective function f between...

function is a bijective holomorphic function whose inverse is also holomorphic. Formally, a biholomorphic function is a function ϕ {\displaystyle \phi } defined...

in the original function space. The transformed function can generally be mapped back to the original function space using the inverse transform. An integral...

antiderivative, inverse derivative, primitive function, primitive integral or indefinite integral of a continuous function f is a differentiable function F whose...

The fundamental theorem of calculus is the statement that differentiation and integration are inverse operations: if a continuous function is first integrated...