Printer Friendly
Dictionary, Encyclopedia and Thesaurus - The Free Dictionary
3,913,337,651 visitors served.
forum Join the Word of the Day Mailing List For webmasters
?
Dictionary/
thesaurus
Medical
dictionary
Legal
dictionary
Financial
dictionary
Acronyms
 
Idioms
Encyclopedia
Wikipedia
encyclopedia
?

implicit function theorem

   Also found in: Wikipedia 0.01 sec.
implicit function theorem [im′plis·ət ¦fəŋk·shən ‚thir·əm]
(mathematics)
A theorem that gives conditions under which an equation in variablesxandymay be solved so as to expressydirectly as a function ofx; it states that ifF(x,y) and ∂F(x,y)/∂yare continuous in a neighborhood of the point (x0,y0) and ifF(x,y) = 0 and ∂F(x,y)/∂y≠ 0, then there is a number ε > 0 such that there is one and only one function ƒf(x) that is continuous and satisfiesF[x,ƒ(x)] = 0 for |x-x0| < ε, and satisfies ƒ(x0) =y0.


Want to thank TFD for its existence? Tell a friend about us, add a link to this page, add the site to iGoogle, or visit the webmaster's page for free fun content.
?Page tools
Printer friendly
Cite / link
Feedback
Mentioned in?  References in periodicals archive?   Encyclopedia browser?   Full browser?
No references found
 
Numerical values Since F is analytic and the Jacobian matrix (I - [partial derivative]F/[partial derivative]Y)(0, 0) is invertible, the implicit function theorem asserts that Y is analytic at 0 (see e.
i] = 0 does not necessarily mean that the function does not exist at this point, because the Implicit Function Theorem establishes sufficient, not necessary, conditions.
After a chapter on general preliminaries, chapters cover differential calculus of boundary perturbations, the implicit function theorem, bifurcation problems, the transversality theorem, generic perturbation of the boundary, boundary operators for second-order elliptic equations, and the method of rapidly oscillating solutions.
 
 
 
Encyclopedia
?

Terms of Use | Privacy policy | Feedback | Advertise with Us | Copyright © 2012 Farlex, Inc.
Disclaimer
All content on this website, including dictionary, thesaurus, literature, geography, and other reference data is for informational purposes only. This information should not be considered complete, up to date, and is not intended to be used in place of a visit, consultation, or advice of a legal, medical, or any other professional.