Difference between r1.18 and the current
@@ -1,3 +1,86 @@
#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 얘긴데https://i.imgur.com/VwkI39E.png
@@ -11,16 +94,17 @@
차분과의 비교: [[미분과_차분]]
[[미분방정식,differential_equation]]
[[미분,differentiation]]
= Sub =
[[VG:전미분,total_differential]]
= tmp =
$F(x)=m\frac{dv}{dt}$
[[미분방정식,differential_equation]]
완전미방(exact DE) 풀이에서, $df=0$ 이면 $f$ 가 상수라는 얘기가 나온다.
완전미방(exact DE) = [[완전미방exact_DE]] = exact_differential_equation 풀이에서, $df=0$ 이면 $f$ 가 [[상수,constant]]라는 얘기가 나온다.
= 미분의 다른 뜻 =
= '미분'의 다른 뜻 =
[[미분,derivative]][[미분,differentiation]]
= Sub =
[[VG:전미분,total_differential]]
[[미분연산자,differentiation_operator]]
[[미분연산자,differentiation_operator]] ?
[[미분연산자,differential_operator]][[미분형식,differential_form]]
= tmp =
$F(x)=m\frac{dv}{dt}$
@@ -29,12 +113,22 @@
$=\left[\frac12mv^2\right]_{v_1}^{v_2}$
$=\frac12mv_2^2-\frac12mv_1^2$
$W_{12}=\Delta K$
from [[http://www.kocw.net/home/search/kemView.do?kemId=324218 6. 에너지 (1)]]
----
Twin: [[VG:미분,differential]]
$=\frac12mv_2^2-\frac12mv_1^2$
즉 우변은 운동에너지(K)의 차이
좌변은 F(x)가 $x_1\to x_2$ 움직이는 동안 한 일
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. [[VG:일-에너지_정리,work-energy_theorem]]
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. }
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]](/wiki/imgs/http.png)
misc ¶
differential = https://www.kms.or.kr/mathdict/list.html?key=ename&keyword=differential{ 2023-10-06 현재 78개. }