"푸크스 미분방정식(Fuchsian differential equation)"의 두 판 사이의 차이
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2013년 1월 14일 (월) 11:31 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
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
관련된 항목들
수학용어번역
- 단어사전 http://www.google.com/dictionary?langpair=en%7Cko&q=
- 발음사전 http://www.forvo.com/search/
- 대한수학회 수학 학술 용어집
- 남·북한수학용어비교
- 대한수학회 수학용어한글화 게시판
사전 형태의 자료
- http://ko.wikipedia.org/wiki/
- http://en.wikipedia.org/wiki/
- http://www.proofwiki.org/wiki/
- http://www.wolframalpha.com/input/?i=
- NIST Digital Library of Mathematical Functions
- The On-Line Encyclopedia of Integer Sequences
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
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
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