Difference between revisions of "Implicit function theorem"
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The '''Implicit Function Theorem''' is a [[theorem]] of [[calculus]]. It states that a (multiple-[[variable]]) function has many [[inverse]]s hidden in different [[neighborhood]]s of the [[image]]. That is to say, the [[graph]] of the function can be finitely [[partition]]ed so that each piece has an inverse function. It is used by [[mathematics|mathematicians]] for local analysis of functions which cannot be globally inverted. It is considered one of the fundaments of the Calculus and does not require [[complex analysis]] for proof. | The '''Implicit Function Theorem''' is a [[theorem]] of [[calculus]]. It states that a (multiple-[[variable]]) function has many [[inverse]]s hidden in different [[neighborhood]]s of the [[image]]. That is to say, the [[graph]] of the function can be finitely [[partition]]ed so that each piece has an inverse function. It is used by [[mathematics|mathematicians]] for local analysis of functions which cannot be globally inverted. It is considered one of the fundaments of the Calculus and does not require [[complex analysis]] for proof. | ||
[[Category:Calculus]] | [[Category:Calculus]] | ||
Revision as of 14:06, January 1, 2009
- It has been proposed that this page, :Implicit function theorem, be titled, "Implicit function theorem".
The Implicit Function Theorem is a theorem of calculus. It states that a (multiple-variable) function has many inverses hidden in different neighborhoods of the image. That is to say, the graph of the function can be finitely partitioned so that each piece has an inverse function. It is used by mathematicians for local analysis of functions which cannot be globally inverted. It is considered one of the fundaments of the Calculus and does not require complex analysis for proof.