푸크스 미분방정식(Fuchsian differential equation)

 

 

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
  

 

 

재미있는 사실

 

• Math Overflow http://mathoverflow.net/search?q=
• 네이버 지식인 http://kin.search.naver.com/search.naver?where=kin_qna&query=

 

 

역사

 

• http://www.google.com/search?hl=en&tbs=tl:1&q=
• 수학사연표
•  

 

 

 

 

관련된 항목들

• 슈워츠 목록
  

 

 

수학용어번역

• 단어사전 http://www.google.com/dictionary?langpair=en%7Cko&q=
• 발음사전 http://www.forvo.com/search/
• 대한수학회 수학 학술 용어집
  
  • http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=eng_term&fstr=
• 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
  
  • http://www.research.att.com/~njas/sequences/?q=

 

 

관련논문

• 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, , in the proceedings of the 1979  Queens University Conference on Number Theory
• 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/BF01157466

 

 

관련도서

• Linear Differential Equations and Group Theory from Riemann to Poincare
  
  • Jeremy J. Gray,  2008(2판)
• 도서내검색
  
  • http://books.google.com/books?q=
  • http://book.daum.net/search/contentSearch.do?query=
• 도서검색
  
  • http://books.google.com/books?q=
  • http://book.daum.net/search/mainSearch.do?query=
  • http://book.daum.net/search/mainSearch.do?query=

 

 

관련기사

• 네이버 뉴스 검색 (키워드 수정)
  
  • http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=
  • http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=
  • http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=

 

 

블로그

• 구글 블로그 검색
  
  • http://blogsearch.google.com/blogsearch?q=
• 네이버 오늘의과학
• Mathematical Moments from the AMS
• BetterExplained