"라플라스-벨트라미 연산자"의 두 판 사이의 차이
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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> | ||
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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> | ||
− | * | + | * 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> |
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− | <h5> | + | <h5>극좌표계의 경우</h5> |
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+ | * [[극좌표계]] | ||
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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
- Math Overflow http://mathoverflow.net/search?q=
- 네이버 지식인 http://kin.search.naver.com/search.naver?where=kin_qna&query=
역사
메모
관련된 항목들
수학용어번역
사전 형태의 자료
- 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://mathworld.wolfram.com/Laplacian.html[1]
- NIST Digital Library of Mathematical Functions
- The On-Line Encyclopedia of Integer Sequences
관련논문
관련도서
- 도서내검색
- 도서검색
관련기사
- 네이버 뉴스 검색 (키워드 수정)