单词	implicit function theorem
释义	implicit function theorem The equation f(x,y) = x2 + y2 – 1 = 0 defines y implicitly in terms of x. At any point of the circle, except (±1,0), the curve can be locally defined as a graph, either or But this is not possible when x = ±1, as the derivative dx/dy is zero. More generally, when a dependent variable y is implicitly related to independent variables x1,x2,…,xk by f(x1,x2,…,xk,y) = 0, then y can be written as a graph y = g(x1,x2,…,xk), local to a point p, if ∂f/∂y(p) ≠ 0. The theorem more generally applies when m dependent variables yi are implicitly defined in terms of n independent variables xi by m equations fi, in which case the Jacobian (∂fi/∂yj) must be invertible.
随便看	total expectation law total force totally bounded totally disconnected total order total probability law total relation totient function touch tower law Tower of Brahma Tower of Hanoi trace tractrix trail trajectory transcendental number transfinite number transformation transformation group transformation matrix transition map transition matrix transitive transitive relation

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