Sub:
{
// TODO mv from 전미분,total_differential and 전미분,total_derivative
}
{
// TODO mv from 전미분,total_differential and 전미분,total_derivative
}
Contents
1. Definition ¶
is a differentiable function.
The differential is defined by the equation
where differential is an independent variable.
The differential is defined by the equation
Note: is a dependent variable; it depends on
2. Definition (Thomas) ¶
Let be a differentiable function.
The differential is an independent variable.
The differential is
The differential is an independent variable.
The differential is
- : 독립변수,independent_variable
- : 항상 와 에 의해 결정되는 종속변수,dependent_variable
즉, 의 값이 주어지면 의 정의역,domain 내의 값에 의해 값이 결정됨.
는 자주 의 변화량 로 선택됨.
4. Definition (utk.edu) ¶
Definition. Let be a differentiable function.
The differential of is an independent variable.
The differential of is defined as
(http://archives.math.utk.edu/visual.calculus/3/differentials.2/index.html)
The differential of is an independent variable.
The differential of is defined as
5. Definition (Varberg) ¶
Definition
Let be a differentiable function of the independent variable
is an arbitrary increment in the independent variable
called the differential of the independent variable is equal to
is the actual change in the variable as changes from to that is,
called the differential of the dependent variable is defined by
called the differential of the independent variable is equal to
is the actual change in the variable as changes from to that is,
called the differential of the dependent variable is defined by
Derivative Rule | Differential Rule |
7. Examples (misc) ¶
이고 를 가정, 그럼 는 어떻게 구하는가?
여기서 은 매우 작으므로 무시하고 양변에서 을 cancel한다. 그러면
// http://kocw.net/home/search/kemView.do?kemId=1215229 이종광 20m
여기서 은 매우 작으므로 무시하고 양변에서 을 cancel한다. 그러면
// http://kocw.net/home/search/kemView.do?kemId=1215229 이종광 20m
로 미분하면
// from 차동우; https://youtu.be/IAIADoy83as?t=246
8. 미소~, ~ 미분소, differential length/area/volume/etc. ¶
기초 calculus에서 중적분(multiple integral)이 나올 때 쓰는 기호는
라 하고
등을 보통 씀. Fubini's theorem에 의해 dx dy dz의 순서를 크게 신경쓰지 않아도 됨.
좌표계,coordinate_system에 따라 달라짐.
미소~ (ex. 미소변위)
~ 미분소 (ex.
극좌표계, 원통좌표계의 미소면적/미소부피는 극좌표계,polar_coordinate_system 참조
~ 미분소 (ex.
선 미분소(differential line), 면적 미분소(differential area), 부피 미분소(differential volume) [1]
체적 미분소(differential volume) , 면적 미분소(differential surface) [2]
길이 미분소(length differential) [3])
선미분소 : 방향을 가진 매우 작은 선분의 극한 [4]체적 미분소(differential volume) , 면적 미분소(differential surface) [2]
길이 미분소(length differential) [3])
구면좌표계의 경우는 구좌표계에서의 미소부피 참조
(Ulaby: CHK, CLEANUP 특히 r, R을 각각 rho, r로 잘 바꾸었는지 check)
(rectangular coord system)
differential surface area:
differential length:
differential area in the
differential surface area:
differential length:
y-z plane:
x-z plane:
x-y plane:
x-z plane:
x-y plane:
(cyl. coord system)
differential volume elements...........?
differential lengths along :
differential length:
differential surface area:
이상 완벽하게 r->rho 바꾸었는지 모르겠음
differential volume elements...........?
differential lengths along :
(φ-z cylindrical surface),
(ρ-z plane),
(ρ-φ plane).
differential volume:(ρ-z plane),
(ρ-φ plane).
(sph. coordinate system)
differential length
vector differential surface
(θ-φ spherical surface),
(r-φ conical surface),
(r-θ plane)
differential volume
(이상 완벽하게 R->r 바꾸었는지 chk)
differential length
(θ-φ spherical surface),
(r-φ conical surface),
(r-θ plane)
(이상 Ulaby 5e, 틀린지 chk)
이하
11. Calculus Made Easy №15(장?) ¶
인데 를 investigate.
우변은 식에 따라 변형하고, 이면
여기서 를 indefinitely small하다고 regard하면, 와 비교해 를 무시할 수 있고, 를 와 같다고 볼 수 있다. 그러면
다음에는 코사인,cosine의 미분.
따라서
따라서
이어서 탄젠트,tangent, 이계미분 나오는데 생략.
13. 기타 ¶
Sub:
{
https://en.wikipedia.org/wiki/Exact_differential
완전미분이 없으면 불완전미분(inexact differential)
완전미분exact_differential
}
완전미분방정식exact de
미분형식,differential_form
{
https://en.wikipedia.org/wiki/Exact_differential
완전미분이 없으면 불완전미분(inexact differential)
완전미분exact_differential
}
완전미분방정식exact de
미분형식,differential_form
선형근사,linear_approximation와 밀접한데 관계 적을 것 TBW
AKA 미분소(素), 디퍼렌셜
Compare:
Sub:
미분,derivative (도함수)
미분,differentiation (도함수를 찾는 것)
무한소,infinitesimal - 비슷?
차분(difference) - see 차이,difference
Up:미분,differentiation (도함수를 찾는 것)
무한소,infinitesimal - 비슷?
차분(difference) - see 차이,difference
Sub:
미분방정식,differential_equation
미분연산자,differentiation_operator (curr at RR 미분연산자,differentiation_operator )
전미분,total_differential
Kaehler_differential =,Kaehler_differential . Kaehler_differential <- German umlaut transliteration을 찾아보면 (ä → ae)라서 pagename 이렇게 해야 할 듯 한데, chk
See also 디퍼렌셜예제가있는페이지미분연산자,differentiation_operator (curr at RR 미분연산자,differentiation_operator )
전미분,total_differential
Kaehler_differential =,Kaehler_differential . Kaehler_differential <- German umlaut transliteration을 찾아보면 (ä → ae)라서 pagename 이렇게 해야 할 듯 한데, chk
{
Kähler differential
https://ko.wikipedia.org/wiki/켈러_미분
https://en.wikipedia.org/wiki/Kähler_differential
https://ja.wikipedia.org/wiki/ケーラー微分
https://ncatlab.org/nlab/show/Kähler differential
...
"Kähler differential"
Kähler differential
Kähler differential
}
Kähler differential
https://ko.wikipedia.org/wiki/켈러_미분
https://en.wikipedia.org/wiki/Kähler_differential
https://ja.wikipedia.org/wiki/ケーラー微分
https://ncatlab.org/nlab/show/Kähler differential
...
"Kähler differential"
Kähler differential
Kähler differential
}
Related: Compare: 차이,difference(=차분)