"Differential Galois theory"의 두 판 사이의 차이
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(피타고라스님이 이 페이지의 이름을 differential Galois theory로 바꾸었습니다.) |
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* Liouville | * Liouville | ||
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| + | <h5>historical origin</h5> | ||
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| + | * integration in finite terms | ||
| + | * quadrature of second order differential equation (Fuchsian differential equation) | ||
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| + | <h5>differential field</h5> | ||
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| 44번째 줄: | 61번째 줄: | ||
* regular singularity | * regular singularity | ||
| − | * indicial equation<br> <br> | + | * indicial equation<br><math>x(x-1)+px+q=0</math><br> <br> |
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| 53번째 줄: | 68번째 줄: | ||
* [http://ocw.mit.edu/NR/rdonlyres/Mathematics/18-034Spring-2007/Readings/notesqd.pdf QD. SOLUTION BY QUADRATURE] | * [http://ocw.mit.edu/NR/rdonlyres/Mathematics/18-034Spring-2007/Readings/notesqd.pdf QD. SOLUTION BY QUADRATURE] | ||
| − | + | * [http://www.caminos.upm.es/matematicas/morales%20ruiz/libroFSB.pdf Differential Galois Theory and Non-Integrability of Hamiltonian Systems] | |
| − | + | * [http://www.caminos.upm.es/matematicas/morales%20ruiz/libroFSB.pdf ][http://www.google.com/url?sa=t&source=web&ct=res&cd=1&ved=0CA4QFjAA&url=http%3A%2F%2Fwww.iop.org%2FEJ%2Fabstract%2F0036-0279%2F38%2F1%2FR01&ei=lC8vS8nOIYqasgPAxYC7BA&usg=AFQjCNEbFgEgKKkYePd8PTExF9JevV6EQA&sig2=kEI9jPaMRI5NgzmUvWr9tA Integrability and non-integrability in Hamiltonian mechanic] | |
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| − | [http://www.caminos.upm.es/matematicas/morales%20ruiz/libroFSB.pdf Differential Galois Theory and Non-Integrability of Hamiltonian Systems] | ||
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| 75번째 줄: | 84번째 줄: | ||
** [[number fields and threefolds]]<br> | ** [[number fields and threefolds]]<br> | ||
** [[3072420|대수적정수론]]<br> | ** [[3072420|대수적정수론]]<br> | ||
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| + | http://www.caminos.upm.es/matematicas/morales%20ruiz/libroFSB.pdf | ||
| 80번째 줄: | 93번째 줄: | ||
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<h5>표준적인 도서 및 추천도서</h5> | <h5>표준적인 도서 및 추천도서</h5> | ||
| 89번째 줄: | 102번째 줄: | ||
** Irving Kaplansky<br> | ** Irving Kaplansky<br> | ||
* algebraic theory of differential equations<br> | * algebraic theory of differential equations<br> | ||
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* http://gigapedia.info/1/galois_theory | * http://gigapedia.info/1/galois_theory | ||
* http://gigapedia.info/1/differential+galois+theory | * http://gigapedia.info/1/differential+galois+theory | ||
| 98번째 줄: | 110번째 줄: | ||
* http://gigapedia.info/1/ | * http://gigapedia.info/1/ | ||
* http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords= | * http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords= | ||
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2009년 12월 31일 (목) 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
- [1]Integrability and non-integrability in Hamiltonian mechanic
하위페이지
http://www.caminos.upm.es/matematicas/morales%20ruiz/libroFSB.pdf
표준적인 도서 및 추천도서
- Abel_s_theorem_by_Arnold.djvu
- arnold book on abel theorem problem 348
- 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=