The purpose of the implicit function theorem is to tell us that functions like g1(x) and g2(x) almost always exist, even in situations where we cannot write down explicit formulas.

外文名 theorem of implicit function 定 义 描述某些变量间是否存在显式关系 应用学科 微积分 相关术语 隐函数

The implicit function theorem gives conditions under which it is possible to solve for x as a function of p in the neighborhood of a known solution ( ̄x, ̄p).

1 The Implicit Function Theorem Suppose that (a; b) is a point on the curve F(x; y) = 0 where and suppose that this equation can be solved for y as a function of x for all (x; y) sufficiently near (a; b).

The Implicit Function Theorem allows us to (partly) reduce impossible questions about systems of nonlinear equations to straightforward questions about systems of linear equations.

Dec 12, 2024 · 在多变量微积分（multivariable calculus）中，隐函数定理（ implicit function theorem） 是一种工具， 它允许将关系转换为多个实变量（relations to be converted to functions of several …

Jan 20, 2024 · So we have from the Implicit Function Theorem that, for z0 6= 0 (and hence x0 6= ±1), there is a continuously differentiable function z = g(x) implicit to the equation x2

Apr 3, 2024 · Theorem The Implicit Function Theorem gives conditions on derivatives which ensure that an implicitly defined set is the graph of a function. Real Functions Let $n$ and $k$ be natural …

在 数学分析 中， 隐函数定理 （英語： Implicit function theorem）是一個用來回答下面的問題的工具： 以 隐函数 表示一個多變量函數，此函數的變量在局部上是否存在显式的关系？

One Equation and Several Independent Variables. The above argument still holds when the variable x is replaced by a vector variable ⃗x = (x1, · · · , xn) in Rn to yield the following implicit function theorem …