"라플라스-벨트라미 연산자"의 두 판 사이의 차이

수학노트
둘러보기로 가기 검색하러 가기
6번째 줄: 6번째 줄:
  
 
<h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">개요</h5>
 
<h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">개요</h5>
 +
 +
*  
  
 
 
 
 
15번째 줄: 17번째 줄:
 
* <math>E=g_{11}</math>, <math>F=g_{12}=g_{21}</math>, <math>G=g_{22}</math>
 
* <math>E=g_{11}</math>, <math>F=g_{12}=g_{21}</math>, <math>G=g_{22}</math>
 
* <math>(g^{ij})=(g_{ij})^{-1}</math>
 
* <math>(g^{ij})=(g_{ij})^{-1}</math>
−
* 라프
+
* 라플라시안<br><math>\Delta f=\nabla_i \nabla^i f =\frac{1}{\sqrt{\det g}} \frac{\partial }{\partial x^j}\left(g^{jk}\sqrt{\det g}\frac{\partial f}{\partial x^k}\right) = g^{jk}\frac{\partial^2 f}{\partial x^j \partial x^k} + \frac{\partial g^{jk}}{\partial x^j} \frac{\partial f}{\partial x^k} + \frac12 g^{jk}g^{il}\frac{\partial g_{il}}{\partial x^j}\frac{\partial f}{\partial x^k}</math><br>
−
* <math>\Delta f=\nabla_i \nabla^i f =\frac{1}{\sqrt{\det g}} \frac{\partial }{\partial x^j}\left(g^{jk}\sqrt{\det g}\frac{\partial f}{\partial x^k}\right) = g^{jk}\frac{\partial^2 f}{\partial x^j \partial x^k} + \frac{\partial g^{jk}}{\partial x^j} \frac{\partial f}{\partial x^k} + \frac12 g^{jk}g^{il}\frac{\partial g_{il}}{\partial x^j}\frac{\partial f}{\partial x^k}</math>
 
  
 
 
 
 
  
−
<h5> </h5>
+
<h5>극좌표계의 경우</h5>
 +
 
 +
* [[극좌표계]]
 +
*  
  
 
 
 
 
77번째 줄: 81번째 줄:
  
 
* http://ko.wikipedia.org/wiki/
 
* http://ko.wikipedia.org/wiki/
 +
* http://en.wikipedia.org/wiki/Laplace_operator
 +
* http://en.wikipedia.org/wiki/List_of_formulas_in_Riemannian_geometry
 +
* http://en.wikipedia.org/wiki/Laplace_operators_in_differential_geometry
 
* http://en.wikipedia.org/wiki/
 
* http://en.wikipedia.org/wiki/
−
* http://www.wolframalpha.com/input/?i=laplacian
+
* http://mathworld.wolfram.com/Laplacian.html[http://www.wolframalpha.com/input/?i=laplacian ]
 
* [http://dlmf.nist.gov/ NIST Digital Library of Mathematical Functions]
 
* [http://dlmf.nist.gov/ NIST Digital Library of Mathematical Functions]
 
* [http://www.research.att.com/%7Enjas/sequences/index.html The On-Line Encyclopedia of Integer Sequences]<br>
 
* [http://www.research.att.com/%7Enjas/sequences/index.html The On-Line Encyclopedia of Integer Sequences]<br>

2010년 1월 11일 (월) 22:21 판

이 항목의 스프링노트 원문주소

 

 

개요
  •  

 

 

제1기본형식을 이용한 표현
  • \(E=g_{11}\), \(F=g_{12}=g_{21}\), \(G=g_{22}\)
  • \((g^{ij})=(g_{ij})^{-1}\)
  • 라플라시안
    \(\Delta f=\nabla_i \nabla^i f =\frac{1}{\sqrt{\det g}} \frac{\partial }{\partial x^j}\left(g^{jk}\sqrt{\det g}\frac{\partial f}{\partial x^k}\right) = g^{jk}\frac{\partial^2 f}{\partial x^j \partial x^k} + \frac{\partial g^{jk}}{\partial x^j} \frac{\partial f}{\partial x^k} + \frac12 g^{jk}g^{il}\frac{\partial g_{il}}{\partial x^j}\frac{\partial f}{\partial x^k}\)

 

극좌표계의 경우

 

 

재미있는 사실

 

 

 

역사

 

 

 

메모

 

 

관련된 항목들

 

 

수학용어번역

 

 

사전 형태의 자료

 

 

관련논문

 

 

관련도서

 

 

관련기사

 

 

블로그
원본 주소 "https://wiki.mathnt.net/index.php?title=라플라스-벨트라미_연산자&oldid=8017"