퍼텐셜함수,potential_function

(정의) 함수 $\vec{F}$ 가 영역 $D$ 에서 정의된 벡터장,vector_field이고,
$D$ 에서 정의된 어떤 스칼라함수,scalar_function $f$ 에 대하여
$\vec{F}=\nabla f$
이면, 함수 $f$ 는 $\vec{F}$ 에 대한 퍼텐셜 함수(potential function)라고 부른다.

(Thomas 13e ko)
어떤 벡터장,vector_field $F$ 에 대해,
$\nabla f=F$
인 미분가능함수,differentiable_function $f$ 가 존재할 때,
이런 $f$ 를 $F$ 의 잠재함수(potential function)라고 한다.
여기서 $\nabla f$ 는 $f$ 의 기울기벡터,gradient_vector를 가리킨다.

Ex. 벡터장 $F(x,y)=\langle 2x,2y \rangle$ 의 경우,
$f(x,y)=x^2+y^2$ 에 대해
$\nabla f=\left\langle \frac{\partial f}{\partial x}, \frac{\partial f}{\partial y} \right\rangle = F$
임을 확인할 수 있으므로, $f$ 는 $F$ 의 잠재함수이다.

(수학백과)

관련있다고 추정: (나중에 적절히 link, related/ see also 등으로)
보존장,conservative_field
curr goto 보존계,conservative_system
보존력,conservative_force



potential_gradient - 한글이름정하면 link later; curr goto 전위


tmp links:


gradient and 잠재함수 (bos의 스터디룸)
https://m.blog.naver.com/bmw9707121/221598732182
{
F = grad f = ∇ f
이면 f는 벡터장 F의 퍼텐셜 함수임.

$F=\operatorname{grad}f=\nabla f$

}

....

벡터장,vector_field $F$ 가 어떤 함수 $f$ 의 기울기,gradient이면, 즉
$\vec{F}=\nabla f$
이면
$\vec{F}$ 는 "conservative vector field" WpKo:보존벡터장 WpEn:Conservative_vector_field .....curr goto 보존계,conservative_system
$f$ 는 퍼텐셜함수

[edit]

Etc


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