In multivariable calculus, the implicit function theorem is a tool which allows relations to be converted to functions. It does this by representing the relation as the graph of a function. There may not be a single function whose graph is the entire relation, but there may be such a function on a restriction of the domain of the relation. The implicit function theorem gives a sufficient condition to ensure that there is such a function.
The theorem states that if the equation (an implicit function) satisfies some mild conditions on its partial derivatives, then one can in principle solve this equation for, at least over some small interval. Geometrically, the locus defined by will overlap locally with the graph of a function (an explicit function, see article on implicit functions).
Famous quotes containing the words implicit, function and/or theorem:
“The vanity of men, a constant insult to women, is also the ground for the implicit feminine claim of superior sensitivity and morality.”
—Patricia Meyer Spacks (b. 1929)
“The mothers and fathers attitudes toward the child correspond to the childs own needs.... Mother has the function of making him secure in life, father has the function of teaching him, guiding him to cope with those problems with which the particular society the child has been born into confronts him.”
—Erich Fromm (19001980)
“To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
—Albert Camus (19131960)