"Differential Galois theory"의 두 판 사이의 차이
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| + | <h5>관련논문</h5> | ||
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| + | * [http://www.jstor.org/stable/2154053 Liouvillian First Integrals of Differential Equations]<br> | ||
| + | ** Michael F. Singer, Transactions of the American Mathematical Society, Vol. 333, No. 2 (Oct., 1992), pp. 673-688 | ||
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<h5>표준적인 도서 및 추천도서</h5> | <h5>표준적인 도서 및 추천도서</h5> | ||
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* Group Theory and Differential Equations<br> | * Group Theory and Differential Equations<br> | ||
| − | ** Lawrence Markus | + | ** Lawrence Markus, 1960 |
* An introduction to differential algebra<br> | * An introduction to differential algebra<br> | ||
** Irving Kaplansky<br> | ** Irving Kaplansky<br> | ||
2010년 1월 1일 (금) 04:57 판
- adele and idele
- differential galois theory
- Liouville
historical origin
- integration in finite terms
- quadrature of second order differential equation (Fuchsian differential equation)
differential field
elementary extension
- using exponential and logarithm
- elementary element
Liouville extension
- we can adjoin integrals and exponentials of integrals + algbraic extension
- an element is said to be representable by a generalized quadrature
Picard-Vessiot extension
- examples
- algebraic extension
- adjoining an integral
- adjoining the exponential of an integral
theorem
If a Picard-Vessiot extension is a Liouville extension, then the Galois group of this extension is solvable.
Fuchsian differential equation
- regular singularity
- indicial equation
\(x(x-1)+px+q=0\)
solution by quadrature
- QD. SOLUTION BY QUADRATURE
- Differential Galois Theory and Non-Integrability of Hamiltonian Systems
- Integrability and non-integrability in Hamiltonian mechanics
하위페이지
http://www.caminos.upm.es/matematicas/morales%20ruiz/libroFSB.pdf
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
표준적인 도서 및 추천도서
- Group Theory and Differential Equations
- Lawrence Markus, 1960
- An introduction to differential algebra
- Irving Kaplansky
- Irving Kaplansky
- algebraic theory of differential equations
- http://gigapedia.info/1/galois_theory
- http://gigapedia.info/1/differential+galois+theory
- http://gigapedia.info/1/Kolchin
- http://gigapedia.info/1/ritt
- http://gigapedia.info/1/Galois'+dream
- http://gigapedia.info/1/differntial+algebra
- http://gigapedia.info/1/
- http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=