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- W77209052 abstract "Suppose we are given a relation in ℝ2 of the form $$Fleft( {x,{rm{ }}y} right){rm{ }} = {rm{ }}0$$ ((14.1)) Then to each value of x there may correspond one or more values of y which satisfy (14.1)—or there may be no values of y which do so. If I = {x: x 0 — h < x < x 0 + h} is an interval such that for each x ∈ I there is exactly one value of y satisfying (14.1), then we say that F(x, y) = 0 defines y as a function of x implicitly on I. Denoting this function by f, we have F[x, f(x)] = 0 for x on I." @default.
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- W77209052 date "1977-01-01" @default.
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- W77209052 title "Implicit function theorems and differentiable maps" @default.
- W77209052 doi "https://doi.org/10.1007/978-1-4615-9990-6_14" @default.
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