"푸크스 미분방정식(Fuchsian differential equation)"의 두 판 사이의 차이
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개요==
메모==
관련논문==
관련도서==
Pythagoras0 (토론 | 기여) 잔글 (찾아 바꾸기 – “</h5>” 문자열을 “==” 문자열로) |
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* [[Fuchsian 미분방정식(Fuchsian differential equation)]]<br> | * [[Fuchsian 미분방정식(Fuchsian differential equation)]]<br> | ||
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* 선형미분방정식<br><math>\frac{d^n w}{dz^n} + A_1(z)\frac{d^{n-1}w}{dz^{n-1}} + \cdots + A_{n-1}(z)\frac{dw}{dz} + A_n(z)w=0</math><br> 모든 특이점이 [[정규특이점(regular singular points)]]인 경우, 이를 Fuchsian 미분방정식이라 한다<br> | * 선형미분방정식<br><math>\frac{d^n w}{dz^n} + A_1(z)\frac{d^{n-1}w}{dz^{n-1}} + \cdots + A_{n-1}(z)\frac{dw}{dz} + A_n(z)w=0</math><br> 모든 특이점이 [[정규특이점(regular singular points)]]인 경우, 이를 Fuchsian 미분방정식이라 한다<br> | ||
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* Group Theory and Differential Equations<br> University of Minnesota Lecture Notes 1959-1960<br> by Lawrence Markus (with permission of the author)<br> | * Group Theory and Differential Equations<br> University of Minnesota Lecture Notes 1959-1960<br> by Lawrence Markus (with permission of the author)<br> | ||
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* [[맴돌이군이 유한인 초기하 미분방정식에 대한 슈바르츠 목록|슈워츠 목록]]<br> | * [[맴돌이군이 유한인 초기하 미분방정식에 대한 슈바르츠 목록|슈워츠 목록]]<br> | ||
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* 단어사전 http://www.google.com/dictionary?langpair=en|ko&q= | * 단어사전 http://www.google.com/dictionary?langpair=en|ko&q= | ||
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* http://ko.wikipedia.org/wiki/ | * http://ko.wikipedia.org/wiki/ | ||
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* [http://www.jstor.org/stable/2154053 Liouvillian First Integrals of Differential Equations]<br> | * [http://www.jstor.org/stable/2154053 Liouvillian First Integrals of Differential Equations]<br> | ||
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* [http://books.google.com/books?id=txinPHIegGgC Linear Differential Equations and Group Theory from Riemann to Poincare]<br> | * [http://books.google.com/books?id=txinPHIegGgC Linear Differential Equations and Group Theory from Riemann to Poincare]<br> | ||
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* 네이버 뉴스 검색 (키워드 수정)<br> | * 네이버 뉴스 검색 (키워드 수정)<br> | ||
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* 구글 블로그 검색<br> | * 구글 블로그 검색<br> | ||
2012년 11월 1일 (목) 08:47 판
이 항목의 스프링노트 원문주소==
개요==
- 선형미분방정식
\(\frac{d^n w}{dz^n} + A_1(z)\frac{d^{n-1}w}{dz^{n-1}} + \cdots + A_{n-1}(z)\frac{dw}{dz} + A_n(z)w=0\)
모든 특이점이 정규특이점(regular singular points)인 경우, 이를 Fuchsian 미분방정식이라 한다
- 19세기에 많은 연구가 진행되었음
- 초기하 미분방정식(Hypergeometric differential equations) 은 대표적인 Fuchsian 미분방정식의 예이다
\(\frac{d^n w}{dz^n} + A_1(z)\frac{d^{n-1}w}{dz^{n-1}} + \cdots + A_{n-1}(z)\frac{dw}{dz} + A_n(z)w=0\)
모든 특이점이 정규특이점(regular singular points)인 경우, 이를 Fuchsian 미분방정식이라 한다
역사==
메모==
- Group Theory and Differential Equations
University of Minnesota Lecture Notes 1959-1960
by Lawrence Markus (with permission of the author)
- http://www.ima.umn.edu/~miller/Group_Theory_and_Differential_Equations.html
University of Minnesota Lecture Notes 1959-1960
by Lawrence Markus (with permission of the author)
관련된 항목들==
수학용어번역==
사전 형태의 자료==
관련논문==
- Liouvillian First Integrals of Differential Equations
- Michael F. Singer, Transactions of the American Mathematical Society, Vol. 333, No. 2 (Oct., 1992), pp. 673-688
- Algebraic Relations Among Solutions of Linear Differential Equations: Fano's Theorem
- Michael F. Singer, American Journal of Mathematics, Vol. 110, No. 1 (Feb., 1988), pp. 115-143
- Elementary and Liouvillian solutions of linear differential equations
- M. F. Singer and J. H. Davenport, 1985
- Some Applications of Linear Groups to Differential Equations
- Michael F. Singer and Marvin D. Tretkoff, American Journal of Mathematics, Vol. 107, No. 5 (Oct., 1985), pp. 1111-1121
- Logarithmic singularities of Fuchs equations, and a criterion for the monodromy group to be finite
- N. V. Grigorenko, MATHEMATICAL NOTESVolume 33, Number 6, 453-454
- Liouvillian Solutions of n-th Order Homogeneous Linear Differential Equations
- Michael F. SingerAmerican Journal of Mathematics, Vol. 103, No. 4 (Aug., 1981), pp. 661-682
- Algebraic Solutions of nth Order Linear Differential Equations
- M. Singer, Proceedings of the Queen's University 1979 Conference on Number Theory, Queens Papers in Pure and Applied Mathematics, (54), pp. 379-420
- On Second Order Linear Differential Equations with Algebraic Solutions
- F. Baldassari, B. Dwork, American Journal of Mathematics, Vol. 101, No. 1 (Feb., 1979), pp. 42-76
- http://www.jstor.org/action/doBasicSearch?Query=fuchsian+differential
- http://www.ams.org/mathscinet
- http://dx.doi.org/10.1007/3-540-15984-3_335
- Michael F. Singer, Transactions of the American Mathematical Society, Vol. 333, No. 2 (Oct., 1992), pp. 673-688
- Michael F. Singer, American Journal of Mathematics, Vol. 110, No. 1 (Feb., 1988), pp. 115-143
- M. F. Singer and J. H. Davenport, 1985
- Michael F. Singer and Marvin D. Tretkoff, American Journal of Mathematics, Vol. 107, No. 5 (Oct., 1985), pp. 1111-1121
- N. V. Grigorenko, MATHEMATICAL NOTESVolume 33, Number 6, 453-454
- Michael F. SingerAmerican Journal of Mathematics, Vol. 103, No. 4 (Aug., 1981), pp. 661-682
- M. Singer, Proceedings of the Queen's University 1979 Conference on Number Theory, Queens Papers in Pure and Applied Mathematics, (54), pp. 379-420
- F. Baldassari, B. Dwork, American Journal of Mathematics, Vol. 101, No. 1 (Feb., 1979), pp. 42-76
관련도서==
- Linear Differential Equations and Group Theory from Riemann to Poincare
- Jeremy J. Gray, 2008(2판)
- Lectures on algebraic solutions of hypergeometric differential equations
- Matsuda, Michihiko, 1985
- 도서내검색
- 도서검색
- Jeremy J. Gray, 2008(2판)
- Matsuda, Michihiko, 1985