Sub:
미분학,differential_calculus?
=미분학,differential_calculus =,differential_calculus 미분학 differential_calculus
{
differential calculus
differential_calculus = https://en.wiktionary.org/wiki/differential_calculus
미분학,differential_calculus?
=미분학,differential_calculus =,differential_calculus 미분학 differential_calculus
{
differential calculus
differential_calculus = https://en.wiktionary.org/wiki/differential_calculus
Sub:
commutative_algebra - 가환대수,commutative_algebra or 가환대수학,commutative_algebra - 에 대한,
Differential_calculus_over_commutative_algebras = https://en.wikipedia.org/wiki/Differential_calculus_over_commutative_algebras
commutative_algebra - 가환대수,commutative_algebra or 가환대수학,commutative_algebra - 에 대한,
Differential_calculus_over_commutative_algebras = https://en.wikipedia.org/wiki/Differential_calculus_over_commutative_algebras미분기하 미분기하학,differential_geometry maybe ... ===미분기하학,differential_geometry =,differential_geometry 미분기하학 differential_geometry
{
differential_geometry
{
differential_geometryTopics
orientation - 향 ? 방향 ? 방향,orientation?
곡률,curvature
법곡률,normal_curvature
주곡률,principal_curvature
곡면,surface
측지선,geodesic or
측지선,geodesic_line ?
다양체,manifold
differential_manifold - 다양체,manifold
torsion - 토션,torsion
스토크스_정리,Stokes_theorem
접속,connection
아핀접속,affine_connection =아핀접속,affine_connection =,affine_connection 아핀접속 affine_connection
orientation - 향 ? 방향 ? 방향,orientation?
곡률,curvature
법곡률,normal_curvature
주곡률,principal_curvature
곡면,surface
측지선,geodesic or
측지선,geodesic_line ?
다양체,manifold
differential_manifold - 다양체,manifold
torsion - 토션,torsion
스토크스_정리,Stokes_theorem
접속,connection
아핀접속,affine_connection =아핀접속,affine_connection =,affine_connection 아핀접속 affine_connection
{
w
affine connection
아핀접속 via
affine connection
affine_connection x 2024-04
MKL 코쥘_접속,Koszul_connection
}//affine connection ...
affine connection 
affine connection
코쥘_접속,Koszul_connectionw
affine connection
아핀접속 via
affine connectionaffine_connection x 2024-04MKL 코쥘_접속,Koszul_connection
}//affine connection ...
affine connection affine connection
선형화,linearization하다가 나온 얘긴데
그림에서
$\displaystyle \Delta x = dx$ 이고
$\displaystyle \Delta y=f(x+\Delta x)-f(x)$ 이고
$\displaystyle dx\approx0\;\Rightarrow\;\Delta y\approx dy$
그래서 $\displaystyle dy=f'(x)dx$ 라고 하는데... 흠.
차분과의 비교: 미분과_차분
미분방정식,differential_equation
완전미방(exact DE) = 완전미방exact_DE = exact_differential_equation 풀이에서, $\displaystyle df=0$ 이면 $\displaystyle f$ 가 상수,constant라는 얘기가 나온다.
완전미방(exact DE) = 완전미방exact_DE = exact_differential_equation 풀이에서, $\displaystyle df=0$ 이면 $\displaystyle f$ 가 상수,constant라는 얘기가 나온다.
Sub ¶
tmp ¶
$\displaystyle F(x)=m\frac{dv}{dt}$
$\displaystyle F(x)dx=m\frac{dv}{dt}dx=mdv\frac{dx}{dt}=mvdv$
$\displaystyle \int_{x_1}^{x_2}F(x)dx=\int_{v_1}^{v_2}mvdv$
좌변은 $\displaystyle F(x)$ 가 $\displaystyle x_1\to x_2$ 움직이는 동안 한 일
$\displaystyle F(x)dx=m\frac{dv}{dt}dx=mdv\frac{dx}{dt}=mvdv$
$\displaystyle \int_{x_1}^{x_2}F(x)dx=\int_{v_1}^{v_2}mvdv$
$\displaystyle =\left[\frac12mv^2\right]_{v_1}^{v_2}$
$\displaystyle =\frac12mv_2^2-\frac12mv_1^2$
즉 우변은 운동에너지,kinetic_energy $\displaystyle K$ 의 차이$\displaystyle =\frac12mv_2^2-\frac12mv_1^2$
좌변은 $\displaystyle F(x)$ 가 $\displaystyle x_1\to x_2$ 움직이는 동안 한 일
$\displaystyle W_{12}=\Delta K$
이것이 일-에너지 정리. 일-에너지_정리,work-energy_theorem - curr
일-에너지_정리,work-energy_theorem
이것이 일-에너지 정리. 일-에너지_정리,work-energy_theorem - curr
일-에너지_정리,work-energy_theorem![[http]](http://www.red-ruby.com/wiki/imgs/http.png)
misc ¶
differential = https://www.kms.or.kr/mathdict/list.html?key=ename&keyword=differential{ 2023-10-06 현재 78개. }