#noindex
Sub:
[[미분학,differential_calculus]]?
=미분학,differential_calculus =,differential_calculus 미분학 differential_calculus
{
'''differential calculus'''
[[WtEn:differential_calculus]] = https://en.wiktionary.org/wiki/differential_calculus

KmsK:미분학
KmsE:gggg

Ndict:미분학
Ggl:미분학

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

KmsE:jjjjj

Ndict:적분학
Ggl:적분학
}


Sub:
[[commutative_algebra]] - [[가환대수,commutative_algebra]] or [[가환대수학,commutative_algebra]] - 에 대한,
[[WpEn:Differential_calculus_over_commutative_algebras]] = https://en.wikipedia.org/wiki/Differential_calculus_over_commutative_algebras

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

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

https://i.imgur.com/VwkI39E.png
그림에서
$\Delta x = dx$ 이고
$\Delta y=f(x+\Delta x)-f(x)$ 이고
$dx\approx0\;\Rightarrow\;\Delta y\approx dy$ 

그래서 $dy=f'(x)dx$ 라고 하는데... 흠.

차분과의 비교: [[미분과_차분]]

[[미분방정식,differential_equation]]
완전미방(exact DE) = [[완전미방exact_DE]] = exact_differential_equation 풀이에서, $df=0$ 이면 $f$ 가 [[상수,constant]]라는 얘기가 나온다.

= '미분'의 다른 뜻 =
[[미분,derivative]]
[[미분,differentiation]]

= Sub =
[[VG:전미분,total_differential]]
[[미분연산자,differentiation_operator]] ?
[[미분연산자,differential_operator]]
[[미분형식,differential_form]]

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

즉 우변은 [[운동에너지,kinetic_energy]] $K$ 의 차이
좌변은 $F(x)$ 가 $x_1\to x_2$ 움직이는 동안 한 일

$W_{12}=\Delta K$
이것이 일-에너지 정리. [[일-에너지_정리,work-energy_theorem]] - curr [[VG:일-에너지_정리,work-energy_theorem]]

from [[http://www.kocw.net/home/search/kemView.do?kemId=324218 6. 에너지 (1)]]

= misc =
관련표현들
minuteness WtEn:minuteness ... [[Calculus_Made_Easy]] 에 자주 나옴

----
[[VG:미분,differential]]

WtEn:differential

[[KmsE:differential]] = https://www.kms.or.kr/mathdict/list.html?key=ename&keyword=differential
{ [[Date(2023-10-06T13:03:03)]] 현재 78개. }