"푸크스 미분방정식(Fuchsian differential equation)"의 두 판 사이의 차이

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==개요==
  
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* 선형미분방정식:<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>
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* 모든 특이점이 [[정칙특이점(regular singular points)]]인 경우, 이를 푸크스 미분방정식이라 한다
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* 19세기에 많은 연구가 진행되었음
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* [[초기하 미분방정식(Hypergeometric differential equations)]] 은 대표적인 푸크스 미분방정식의 예이다
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==역사==
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* http://www.google.com/search?hl=en&tbs=tl:1&q=
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* [[수학사 연표]]
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* 
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==메모==
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* Dwork family http://www.math.sunysb.edu/~cschnell/pdf/notes/picardfuchs.pdf
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*  Group Theory and Differential Equations University of Minnesota Lecture Notes 1959-1960 by Lawrence Markus  (with permission of the author)
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* http://www.ima.umn.edu/~miller/Group_Theory_and_Differential_Equations.html
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==관련된 항목들==
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* [[르장드르의 타원곡선 모임]]
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* [[맴돌이군이 유한인 초기하 미분방정식에 대한 슈바르츠 목록]]
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==수학용어번역==
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*{{forvo|url=Fuchs}}
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==에세이==
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* Gray, J. J. 1984. “Fuchs and the Theory of Differential Equations.” Bulletin of the American Mathematical Society 10 (1): 1–26. doi:[http://dx.doi.org/10.1090/S0273-0979-1984-15186-3  10.1090/S0273-0979-1984-15186-3].
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==관련논문==
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* [http://www.jstor.org/stable/2154053 Liouvillian First Integrals of Differential Equations]
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** Michael F. Singer, Transactions of the American Mathematical Society, Vol. 333, No. 2 (Oct., 1992), pp. 673-688
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* [http://www.jstor.org/stable/2374541 Algebraic Relations Among Solutions of Linear Differential Equations: Fano's Theorem]
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** Michael F. Singer, American Journal of Mathematics, Vol. 110, No. 1 (Feb., 1988), pp. 115-143
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* [http://dx.doi.org/10.1007/3-540-15984-3_335 Elementary and Liouvillian solutions of linear differential equations]
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** M. F. Singer and J. H. Davenport, 1985
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* [http://www.jstor.org/stable/2374348 Some Applications of Linear Groups to Differential Equations]
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** Michael F. Singer and Marvin D. Tretkoff, American Journal of Mathematics, Vol. 107, No. 5 (Oct., 1985), pp. 1111-1121
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*  L[http://dx.doi.org/10.1007/BF01157466 ogarithmic singularities of Fuchs equations, and a criterion for the monodromy group to be finite]
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** N. V. Grigorenko, MATHEMATICAL NOTESVolume 33, Number 6, 453-454
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* [http://www.jstor.org/stable/2374045 Liouvillian Solutions of n-th Order Homogeneous Linear Differential Equations]
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** Michael F. SingerAmerican Journal of Mathematics, Vol. 103, No. 4 (Aug., 1981), pp. 661-682
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*  Algebraic Solutions of nth Order Linear Differential Equations
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** M. Singer, Proceedings of the Queen's University 1979 Conference on Number Theory, Queens Papers in Pure and Applied Mathematics, (54), pp. 379-420
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* [http://www.jstor.org/stable/2373938 On Second Order Linear Differential Equations with Algebraic Solutions]
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** F. Baldassari, B. Dwork, American Journal of Mathematics, Vol. 101, No. 1 (Feb., 1979), pp. 42-76
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==관련도서==
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* [http://books.google.com/books?id=txinPHIegGgC Linear Differential Equations and Group Theory from Riemann to Poincare]
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** Jeremy J. Gray,  2008(2판)
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* [http://repository.kulib.kyoto-u.ac.jp/dspace/handle/2433/84920 Lectures on algebraic solutions of hypergeometric differential equations]
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** Matsuda, Michihiko, 1985
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[[분류:미분방정식]]

2013년 11월 22일 (금) 07:12 기준 최신판

개요



역사



메모



관련된 항목들



수학용어번역

  • Fuchs - 발음사전 Forvo



에세이

  • Gray, J. J. 1984. “Fuchs and the Theory of Differential Equations.” Bulletin of the American Mathematical Society 10 (1): 1–26. doi:10.1090/S0273-0979-1984-15186-3.



관련논문



관련도서

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