미분,differential

Difference between r1.28 and the current

@@ -33,6 +33,53 @@
"differential calculus"
Ggl:"differential calculus"
} // differential calculus
 
미분기하 [[미분기하학,differential_geometry]] maybe ... ===미분기하학,differential_geometry =,differential_geometry 미분기하학 differential_geometry
{
WtEn:differential_geometry
 
MKL
[[미분,differential]]
derivative
[[미분,derivative]]
[[도함수,derivative]]
[[해석학,analysis]]
[[미적분,calculus]]
[[기하학,geometry]]
 
Topics
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]]
{
w
MKL
[[올,fiber]]
[[다발,bundle]]
}
[[아핀접속,affine_connection]] =아핀접속,affine_connection =,affine_connection 아핀접속 affine_connection
{
w
'''affine connection'''
아핀접속 via KmsE:"affine connection"
WtEn:affine_connection x 2024-04
MKL [[코쥘_접속,Koszul_connection]]
}//affine connection ... NN:"affine connection" Ggl:"affine connection"
[[코쥘_접속,Koszul_connection]]
 
 
Namu:미분기하학
} // 미분기하학 ... NN:미분기하학 Ggl:미분기하학
----
[[선형화,linearization]]하다가 나온 얘긴데


Sub:
미분학,differential_calculus?
=미분학,differential_calculus =,differential_calculus 미분학 differential_calculus
{
differential calculus
WtEn:differential_calculus = https://en.wiktionary.org/wiki/differential_calculus



opp 적분학 integral_calculus ?
{
WtEn:integral_calculus = ffff
KmsK:적분학





합쳐서 미적분학 = 미적분,calculus? - 칼큘러스,calculus

"differential calculus"
Ggl:differential calculus
} // differential calculus

미분기하 미분기하학,differential_geometry maybe ... ===미분기하학,differential_geometry =,differential_geometry 미분기하학 differential_geometry
{
WtEn:differential_geometry





선형화,linearization하다가 나온 얘긴데

https://i.imgur.com/VwkI39E.png

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.

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'미분'의 다른 뜻

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Sub

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tmp

$\displaystyle F(x)=m\frac{dv}{dt}$
$\displaystyle F(x)dx=m\frac{dv}{dt}dx=mdv\frac{dx}{dt}=mvdv$
$\displaystyle \int_{x_1}^{x_2}F(x)dx=\int_{v_1}^{v_2}mvdv$
$\displaystyle =\left[\frac12mv^2\right]_{v_1}^{v_2}$
$\displaystyle =\frac12mv_2^2-\frac12mv_1^2$

즉 우변은 운동에너지,kinetic_energy $\displaystyle K$ 의 차이
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 VG:일-에너지_정리,work-energy_theorem


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misc

미분,differential Modified on 4:48 am, April 5, 2024.
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