"스텀-리우빌 이론"의 두 판 사이의 차이
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Pythagoras0 (토론 | 기여) |
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| (사용자 2명의 중간 판 24개는 보이지 않습니다) | |||
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| − | + | ==이 항목의 스프링노트 원문주소== | |
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| − | + | ==개요== | |
| − | <math> | + | * [[이계 선형 미분방정식|이계 선형 미분방정]]식:<math>-\frac{d}{dx}\left[p(x)\frac{dy}{ dx}\right]+q(x)y=\lambda w(x)y</math> |
| + | * 많은 직교다항식들을 이해하는 이론적 틀 | ||
| + | * 편미분방정식의 변수분리를 통해 얻어지는 상미분방정식에서 많이 나타남 | ||
| + | * 양자역학의 1차원 슈뢰딩거 방정식에 중요 | ||
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| − | + | ==Self-adjoint== | |
| + | |||
| + | <math>(Lf, g)=\int^b_a (pf'' + qf' + rf)\bar{g}dx </math>:<math>= pf'\bar{g}|_a^b - \int^b_a f'(p\bar{g})'dx + qf\bar{g}|_a^b-\int_a^b f(q\bar{g})'dx +\int_a^b fr\bar{g}dx</math> | ||
| + | |||
| + | <math>=[pf'\bar{g} -f(p\bar{g})']|_a^b +\int_a^b f(p\bar{g})''dx + qf \bar{g}|^b_a-\int_a^b f(q\bar{g})'dx +\int_a^b fr\bar{g}dx </math> | ||
| + | |||
| + | <math>= (f, (\bar{p}g)'' - (\bar{q}g)' + \bar{r}g) + [p(f'\bar{g} - f \bar{g}') + (q - p')f \bar{g}]|^b_a</math> | ||
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| + | ==재미있는 사실== | ||
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* 네이버 지식인 http://kin.search.naver.com/search.naver?where=kin_qna&query= | * 네이버 지식인 http://kin.search.naver.com/search.naver?where=kin_qna&query= | ||
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| − | + | ==역사== | |
| − | * [[ | + | * [[수학사 연표]] |
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| − | + | ==메모== | |
| − | + | * [http://astro.berkeley.edu/%7Emwhite/teachdir/sturmliouville.pdf http://astro.berkeley.edu/~mwhite/teachdir/sturmliouville.pdf] | |
| + | * [http://www.math.ucdavis.edu/%7Ehunter/m280_09/ch4.pdf http://www.math.ucdavis.edu/~hunter/m280_09/ch4.pdf] | ||
| + | * [http://physics.ubc.ca/%7Eberciu/TEACHING/PHYS312/LECTURES/ste.pdf http://physics.ubc.ca/~berciu/TEACHING/PHYS312/LECTURES/ste.pdf] | ||
| − | + | ||
| − | + | ==관련된 항목들== | |
| − | + | ||
| − | + | ||
| − | + | ==수학용어번역== | |
* http://www.google.com/dictionary?langpair=en|ko&q= | * http://www.google.com/dictionary?langpair=en|ko&q= | ||
| − | * [http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=&fstr= 대한수학회 수학 학술 용어집] | + | * [http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=&fstr= 대한수학회 수학 학술 용어집] |
** http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=eng_term&fstr= | ** http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=eng_term&fstr= | ||
| − | * [http://kms.or.kr/home/kor/board/bulletin_list_subject.asp?bulletinid=%7BD6048897-56F9-43D7-8BB6-50B362D1243A%7D&boardname=%BC%F6%C7%D0%BF%EB%BE%EE%C5%E4%B7%D0%B9%E6&globalmenu=7&localmenu=4 | + | * [http://kms.or.kr/home/kor/board/bulletin_list_subject.asp?bulletinid=%7BD6048897-56F9-43D7-8BB6-50B362D1243A%7D&boardname=%BC%F6%C7%D0%BF%EB%BE%EE%C5%E4%B7%D0%B9%E6&globalmenu=7&localmenu=4 대한수학회 수학용어한글화 게시판] |
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| − | + | ==사전 형태의 자료== | |
| + | * [http://ko.wikipedia.org/wiki/%EC%8A%A4%ED%85%80-%EB%A6%AC%EC%9A%B0%EB%B9%8C_%EC%9D%B4%EB%A1%A0 http://ko.wikipedia.org/wiki/스텀-리우빌_이론] | ||
* http://ko.wikipedia.org/wiki/ | * http://ko.wikipedia.org/wiki/ | ||
* [http://en.wikipedia.org/wiki/Sturm%E2%80%93Liouville_theory http://en.wikipedia.org/wiki/Sturm–Liouville_theory] | * [http://en.wikipedia.org/wiki/Sturm%E2%80%93Liouville_theory http://en.wikipedia.org/wiki/Sturm–Liouville_theory] | ||
| 59번째 줄: | 79번째 줄: | ||
* http://www.wolframalpha.com/input/?i= | * http://www.wolframalpha.com/input/?i= | ||
* [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] | + | * [http://www.research.att.com/%7Enjas/sequences/index.html The On-Line Encyclopedia of Integer Sequences] |
** http://www.research.att.com/~njas/sequences/?q= | ** http://www.research.att.com/~njas/sequences/?q= | ||
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| − | + | ==관련논문== | |
| + | * L�tzen, Jesper. 1984. Sturm and Liouville's work on ordinary linear differential equations. The emergence of Sturm-Liouville theory. Archive for History of Exact Sciences 29, no. 4: 309-376. doi:[http://dx.doi.org/10.1007/BF00348405 10.1007/BF00348405]. | ||
| + | * [http://www.math.niu.edu/SL2/papers/birk0.pdf A Catalogue of Sturm-Liouville differential equations] | ||
| + | ** WN Everitt | ||
* http://www.jstor.org/action/doBasicSearch?Query= | * http://www.jstor.org/action/doBasicSearch?Query= | ||
* http://dx.doi.org/ | * http://dx.doi.org/ | ||
| − | + | ||
| − | + | ==관련도서== | |
| − | * 도서내검색 | + | * Sturm-Liouville Theory and its Applications |
| + | ** Mohammed Abdelrahman Al-Gwaiz | ||
| + | * 도서내검색 | ||
** http://books.google.com/books?q= | ** http://books.google.com/books?q= | ||
** http://book.daum.net/search/contentSearch.do?query= | ** http://book.daum.net/search/contentSearch.do?query= | ||
| − | * 도서검색 | + | * 도서검색 |
** http://books.google.com/books?q= | ** http://books.google.com/books?q= | ||
** http://book.daum.net/search/mainSearch.do?query= | ** http://book.daum.net/search/mainSearch.do?query= | ||
** http://book.daum.net/search/mainSearch.do?query= | ** http://book.daum.net/search/mainSearch.do?query= | ||
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| − | + | ==블로그== | |
| + | [[분류:미분방정식]] | ||
| − | + | ==메타데이터== | |
| − | + | ===위키데이터=== | |
| − | * [ | + | * ID : [https://www.wikidata.org/wiki/Q1154082 Q1154082] |
| − | * [ | + | ===Spacy 패턴 목록=== |
| − | * [ | + | * [{'LOWER': 'sturm'}, {'OP': '*'}, {'LOWER': 'liouville'}, {'LEMMA': 'theory'}] |
| − | * | + | * [{'LOWER': 'sturm'}, {'OP': '*'}, {'LOWER': 'liouville'}, {'LEMMA': 'equation'}] |
2021년 2월 17일 (수) 05:50 기준 최신판
이 항목의 스프링노트 원문주소
개요
- 이계 선형 미분방정식\[-\frac{d}{dx}\left[p(x)\frac{dy}{ dx}\right]+q(x)y=\lambda w(x)y\]
- 많은 직교다항식들을 이해하는 이론적 틀
- 편미분방정식의 변수분리를 통해 얻어지는 상미분방정식에서 많이 나타남
- 양자역학의 1차원 슈뢰딩거 방정식에 중요
Self-adjoint
\((Lf, g)=\int^b_a (pf'' + qf' + rf)\bar{g}dx \)\[= pf'\bar{g}|_a^b - \int^b_a f'(p\bar{g})'dx + qf\bar{g}|_a^b-\int_a^b f(q\bar{g})'dx +\int_a^b fr\bar{g}dx\]
\(=[pf'\bar{g} -f(p\bar{g})']|_a^b +\int_a^b f(p\bar{g})''dx + qf \bar{g}|^b_a-\int_a^b f(q\bar{g})'dx +\int_a^b fr\bar{g}dx \)
\(= (f, (\bar{p}g)'' - (\bar{q}g)' + \bar{r}g) + [p(f'\bar{g} - f \bar{g}') + (q - p')f \bar{g}]|^b_a\)
재미있는 사실
역사
메모
- http://astro.berkeley.edu/~mwhite/teachdir/sturmliouville.pdf
- http://www.math.ucdavis.edu/~hunter/m280_09/ch4.pdf
- http://physics.ubc.ca/~berciu/TEACHING/PHYS312/LECTURES/ste.pdf
관련된 항목들
수학용어번역
사전 형태의 자료
- http://ko.wikipedia.org/wiki/스텀-리우빌_이론
- http://ko.wikipedia.org/wiki/
- http://en.wikipedia.org/wiki/Sturm–Liouville_theory
- http://en.wikipedia.org/wiki/
- http://www.wolframalpha.com/input/?i=
- NIST Digital Library of Mathematical Functions
- The On-Line Encyclopedia of Integer Sequences
관련논문
- L�tzen, Jesper. 1984. Sturm and Liouville's work on ordinary linear differential equations. The emergence of Sturm-Liouville theory. Archive for History of Exact Sciences 29, no. 4: 309-376. doi:10.1007/BF00348405.
- A Catalogue of Sturm-Liouville differential equations
- WN Everitt
- http://www.jstor.org/action/doBasicSearch?Query=
- http://dx.doi.org/
관련도서
- Sturm-Liouville Theory and its Applications
- Mohammed Abdelrahman Al-Gwaiz
- 도서내검색
- 도서검색
블로그
메타데이터
위키데이터
- ID : Q1154082
Spacy 패턴 목록
- [{'LOWER': 'sturm'}, {'OP': '*'}, {'LOWER': 'liouville'}, {'LEMMA': 'theory'}]
- [{'LOWER': 'sturm'}, {'OP': '*'}, {'LOWER': 'liouville'}, {'LEMMA': 'equation'}]