- 디그리,degree . . . . 41 matches
[[동차다항식,homogeneous_polynomial]] =동차다항식,homogeneous_polynomial =,homogeneous_polynomial . (w)
[[WtEn:homogeneous_polynomial]] = https://en.wiktionary.org/wiki/homogeneous_polynomial
[[WpEn:Homogeneous_polynomial]] = https://en.wikipedia.org/wiki/Homogeneous_polynomial
KmsE:"homogeneous polynomial"
Ggl:"homogeneous polynomial"
"homogeneous polynomial"
[[동차함수,homogeneous_function]] =동차함수,homogeneous_function ? =,homogeneous_function ? (w)
WtEn:homogeneous_function
[[WtEn:homogeneous_function]]
= https://en.wiktionary.org/wiki/homogeneous_function
[[WpEn:Homogeneous_function]]
= https://en.wikipedia.org/wiki/Homogeneous_function
https://mathworld.wolfram.com/HomogeneousFunction.html
https://encyclopediaofmath.org/wiki/Homogeneous_function
이것에 대한 오일러의 정리 : https://mathworld.wolfram.com/EulersHomogeneousFunctionTheorem.html
KmsE:"homogeneous function"
Ggl:"homogeneous function"
"homogeneous function"
Degree two인 homogeneous polynomial/function(2차 동차다항식/동차함수)는 [[이차형식,quadratic_form]]과 밀접 - tbw 명확히.
그리고 다음도 cf. (모두 local에 =,homogeneous =,homogeneity =,homogeneousness (RR page: [[동차성,homogeneity]]) 저기에 순서대로)
- 미분방정식,differential_equation . . . . 33 matches
2계 미방을 다음과 같이 가정한다. $\alpha$ 는 실수 parameter. 이건 homogeneous - 왜냐면 (x 또는 (x의 도함수))에 독립인, 순수하게 시간종속인(time-dependent) term이 0이기 때문.
[[제차미방homogeneous_DE]] -> [[동차미분방정식,homogeneous_differential_equation]]
DE에서 $y=0$ 이 해이면 '''homogeneous DE'''임.
A differential equation is '''homogeneous''' if $y=0$ is a solution.
[[동차미분방정식,제차미분방정식,homogeneous_differential_equation]]
[[비제차미방nonhomogeneous_DE]]
[[비제차상미방nonhomogeneous_ODE]] 의 일반해는 $y=y_h+y_p$
제차 homogeneous
비제차 inhomogeneous
= 2계 선형 with 상수 계수: The Homogeneous Case (ess. eng. math) =
= 2계 선형 with 상수 계수: The Inhomogeneous Case (ess. eng. math) =
: 제차선형미분방정식 (homogeneous)
: 비제차선형미분방정식 (non-homogeneous)
$y'+p(x)y=0$ : (1)의 homogeneous equation ........(2)
이러면 $\mu$ 에 대한 1계 선형미분방정식 형태가 된다. (+homogeneous)
일단 homogeneous의 개념을 확장.
이변수함수 $f(x,y)$ 가 homogeneous of degree $n$
$f(x,y)=x^2+y^2$ : 2차 homogeneous
$f(x,y)=x^3+2xy^2$ : 3차 homogeneous? CHK
$f(x,y)=\sqrt{x^2+y^2}$ : 1차 homogeneous
- 공간,space . . . . 14 matches
== homogeneous space ==
[[homogeneous_space]] =,homogeneous_space =,homogeneous_space . homogeneous_space
동차공간, 동질공간 (kms) KmsE:"homogeneous space"
[[WtEn:homogeneous_space]] = https://en.wiktionary.org/wiki/homogeneous_space
[[WpEn:Homogeneous_space]] = https://en.wikipedia.org/wiki/Homogeneous_space
Ndict:"homogeneous space"
Bing:"homogeneous space"
Ggl:"homogeneous space"
"homogeneous space"
- 형용사,adjective . . . . 14 matches
https://en.wiktionary.org/wiki/bihomogeneous .... n. ?
(...examples:) https://en.wikipedia.org/wiki/Homogeneous_relation#Operations
##=,homogeneous .
homogeneous // KmsE:homoge WtEn:homogeneous
bihomogeneous WtEn:bihomogeneous
homogeneous_relation
homogeneous relation
WtEn:homogeneous_relation
WpEn:Homogeneous_relation
Ggl:"homogeneous relation"
"homogeneous relation"
Srch:homogeneous
- 해,solution . . . . 12 matches
[[homogeneous_solution]] =,homogeneous_solution =,homogeneous_solution . homogeneous_solution
WtEn:homogeneous_solution
homogeneous adj. WtEn:homogeneous -> n. WtEn:homogeneousness / WtEn:homogeneity ... [[homogeneity]] NdEn:homogeneity Ggl:homogeneity
= 제차해 / 동차해 / homogeneous solution =
[[homogeneous_solution]]
과도해 transient_solution = 제차해 동차해 homogeneous_solution : [[입력,input]]이 [[영,zero]]일 때의 [[반응,response]].
일반적으로 미분방정식의 해는 등차해^^homogeneous solution^^와 특수해^^particular solution^^의 합으로 표현할 수 있다.
- 동차미분방정식,제차미분방정식,homogeneous_differential_equation . . . . 11 matches
에서 $M(x,y)$ 와 $N(x,y)$ 가 같은 차수인 [[동차함수,homogeneous_function]]일 때 '''동차미분방정식'''이라 한다.
QQQ 1 : [[선형미방linear_DE]]에서만 homogeneous_DE 가 정의되는건지 아님 다른 경우가 있는지?
en nonhomogeneous 로 할지 inhomogeneous 로 할지.. Google:equation+nonhomogeneous+vs+inhomogeneous
그리고 homogeneous에는 다른 뜻도 있는데, [[동차함수,homogeneous_function]] ... local에 작성중.
// Srch VG: "homogeneous_function"을(를) 전체 찾아보기: [[http://tomoyo.ivyro.net/123/wiki.php/asdf?action=fullsearch&value=homogeneous_function&context=20&case=1]]
--''페이지가 너무 긴데 mv to [[동차미방homogeneous_DE]]?''--
- 공학수학1,engineering_mathematics_1 . . . . 10 matches
homogeneous: g(x)=0
nonhomogeneous: g(x)≠0
$y_c$ 는 homogeneous equation $y'+p(x)y=0$ 의 general solution.
(homogeneous equation의 solution이다 라고 해서, $y_h$ 로 쓰기도 한다.)
1. Solve the homogeneous DE that is separable:
2. Find a solution of nonhomogeneous DE $y_p$ that is independent with $y_c(x)$ .
1. Solve the homogeneous DE that is separable:
즉 particular solution이 아니라 homogeneous equation의 solution이 되버리는 것이다.
2. Find a solution of nonhomogeneous DE $y_p$ that is independent with $y_c(x)$ .
- the solution of nonhomogeneous DE:
- 관계,relation . . . . 10 matches
endorelation 으로 정의함. 그게뭐야? not in ndict. 구글해보니 aka homogeneous_relation.
== homogeneous relation / endorelation ==
[[homogeneous_relation]] =,homogeneous_relation . homogeneous_relation
homogeneous relation
https://en.wikipedia.org/wiki/Homogeneous_relation
Ggl:"homogeneous relation"
''WpEn:Universal_relation redir. to: WpEn:Homogeneous_relation#Particular_homogeneous_relations''
- 마르코프_연쇄,Markov_chain . . . . 5 matches
time-homogeneous_Markov_chain =,time-homogeneous_Markov_chain =,time-homogeneous_Markov_chain . time-homogeneous_Markov_chain
time-homogeneous Markov chain
- 이차형식,quadratic_form . . . . 3 matches
= Rel: homogeneous/homogeneity/degree =
[[동차다항식,homogeneous_polynomial]] [[동차함수,homogeneous_function]] ...에서, [[디그리,degree]] or [[차수,degree]]가 2인 경우와 밀접한데 tbw
- 항등함수,identity_function . . . . 3 matches
https://en.wikipedia.org/wiki/Homogeneous_relation#Particular_homogeneous_relations
이건 [[homogeneous_relation]] also called [[endorelation]]의 일종임.
- 형식,form . . . . 3 matches
"form" is another name for a homogeneous polynomial[* WpEn:Quadratic_form 처음 부분]
즉, '''형식'''이란 [[동차다항식,homogeneous_polynomial]]의 다른 이름이다.
WpEn:Homogeneous_polynomial
- 선형시스템,linear_system . . . . 2 matches
또한 x,,1,,(t)를 상수배만큼 곱한 신호, 즉 x(t)=αx,,1,,(t)를 입력시키는 경우, 출력도 동일한 비율로 곱해져서 출력된다면, 즉 y(t)=αy,,1,,(t)가 된다면 이 시스템을 균일적(homogeneous)이라고 부른다.
// homogeneous_system
- 유니버스,universe . . . . 2 matches
* homogeneous - [[균질성]] [[동질성]] [homogeneity] [homogeneousness] .. KpsE:homogen
- degree . . . . 1 match
cf. [[동차다항식,homogeneous_polynomial]]
- 미분연산자,differentiation_operator . . . . 1 match
Zill 6e 3.1.2 Homogeneous Equations
- 방정식,equation . . . . 1 match
[[동차미분방정식,제차미분방정식,homogeneous_differential_equation]]
- 부분공간,subspace . . . . 1 match
부분공간의 동차연립방정식 ( homogeneous system of equations? ) Ax=0의 [[해,solution]]로 이루어진 공간 - 영공간(null space)
- 연결,connection . . . . 1 match
{"In math, a [[relation_on_a_set]]{link to: WpEn:Relation_on_a_set ''redir to WpEn:Binary_relation#Homogeneous_relation '' }
- 최정환_미분방정식및연습_2013 . . . . 1 match
2nd order linear homogeneous equation with constant coefficients
- 코시오일러방정식Cauchy-Euler_equation . . . . 1 match
homogeneous second-order equation:
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