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Topic: Implicit function theorem

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Singular point of an algebraic variety

Oscar Zariski

List of Japanese people

	PlanetMath: implicit function theorem
		The inverse function theorem is a special case of the implicit function theorem where the dimension of each variable is the same.
		This is version 8 of implicit function theorem, born on 2002-08-24, modified 2004-05-25.
		I assume it is the derivative with resepect to the jth component of the argument, but it would be nice to have it defined or cross-referenced.
	planetmath.org /encyclopedia/ImplicitFunctionTheorem.html (207 words)

	Calculus Tutorials and Problems
		Graphical interpretation of the derivative of a function is explored interactively using an applet.
		The definition of the derivative of a function in calculus is explored interactively using an applet.
		Theorems, related to the continuiy of functions and their uses in calculus, are presented and dicussed with examples.
	www.analyzemath.com /calculus.html (1447 words)

	Implicit function theorem: Facts and details from Encyclopedia Topic (Site not responding. Last check: 2007-10-27)
		This means that y cannot therefore be a differentiable function Derivative quick summary:
		In mathematics, the derivative of a function is one of the two central concepts of calculus....
		(a saddle point is a point of a function of two variables which is a stationary point but not a local extremum....
	www.absoluteastronomy.com /encyclopedia/i/im/implicit_function_theorem.htm (816 words)

	Manifold - Wikipedia, the free encyclopedia
		Viewed using calculus, the circle transition function T is simply a function between open intervals, which gives a meaning to the statement that T is differentiable.
		Differentiable manifolds have homeomorphisms on overlapping neighborhoods diffeomorphic with each other, so that the manifold has a well-defined set of functions which are differentiable in each neighborhood, and so differentiable on the manifold as a whole.
		As the transition map is a smooth function, this atlas defines a smooth manifold.
	en.wikipedia.org /wiki/Manifold (5693 words)

	Implicit function theorem - All About All (Site not responding. Last check: 2007-10-27)
		In mathematics, in the field of calculus of several variables, the implicit function theorem says that for a suitable set of equations, some of the variables are defined as functions of the others.
		There are some natural limitations on this use of a mathematical relation to define implicit functions, which may be seen in trying to use the unit circle as the graph of a function.
		The implicit function is only locally defined, and points at which the first-order behavior would be problematic are outside the scope of the result.
	www.answers-zone.com /article/Implicit_function_theorem (602 words)

	Differentiation of functions,limits (II), maximum, minimum, inflection points.
		The theorem says that there is a suitable point R on the curve C such that the tangent line in R is parallel to PQ.
		Suppose that a function is differentiable in ]t-e,t+e[.
		This function is continious in [a,b] and the derivative exists in ]a,b[.
	ddart.net /science/mathmatics/mathtutorial/diff.htm (2811 words)

	Douglas S. Bridges
		`On the isolation of zeroes of an analytic function', Pacific J. Math.
		`A recursive counterexample to Debreu's theorem on the existence of a utility function' (with Fred Richman), Math.
		`The constructive implicit function theorem and applications in physics' (with C. Calude, B. Pavlov, and D. Stefanescu), Chaos, Solitons & Fractals 10(6), 927- 934, 1999.
	www.math.canterbury.ac.nz /~mathdsb/complete.html (1915 words)

	No Title
		Holomorphic functions of bounded mean oscillation and mapping properties of the Szegö projection, Duke Math.
		Functions of Several Complex Variables and Analytic Spaces, The Encyclopedia of Physical Science and Technology, Academic Press, v.
		Fatou theorems old and new: an overview of the boundary behavior of holomorphic functions, Proceedings of a Conference on Several Complex Variables, Seoul National University, 2000.
	www.math.wustl.edu /~sk/total/total.html (3548 words)

	[No title]
		D. Sun and J. Sun, ``Loewner's operator and spectral functions in Euclidean Jordan algebras," December 2004.
		Y.B. Zhao and D. Sun, ``Alternative theorems for nonlinear projection equations and their applications to generalized complementarity problems'', Nonlinear Analysis: Theory, Methods and Applications.
		Sun and J. Han, ``On a conjecture in Moreau-Yosida approximation of a nonsmooth convex function'' Chinese Science Bulletin 42 (1997) 1423--1426.
	www.math.nus.edu.sg /~matsundf (1528 words)

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