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imported>Pythagoras0 (새 문서: ==list== * https://www.youtube.com/watch?v=LYNOGk3ZjFM&list=PLB24487A8C5EDC02A ==lecture 1 perturbation method== * solve $x^5+x=1$ ===method 1=== * try $x^5+\epsilon x=1$ * find $x(...) |
imported>Pythagoras0 |
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| 23번째 줄: | 23번째 줄: | ||
* yes, for example, Pade summation can be used | * yes, for example, Pade summation can be used | ||
| + | ==books== | ||
| + | * Bender, Carl M., and Steven A. Orszag. 1999. Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Methods and Perturbation Theory. Springer. | ||
[[분류:talks and lecture notes]] | [[분류:talks and lecture notes]] | ||
2014년 2월 27일 (목) 10:32 판
list
lecture 1 perturbation method
- solve $x^5+x=1$
method 1
- try $x^5+\epsilon x=1$
- find $x(\epsilon)$ satisfying $x(\epsilon)^5+\epsilon x(\epsilon)=1$
- answer
$$x(\epsilon)=1-\frac{\epsilon }{5}-\frac{\epsilon ^2}{25}-\frac{\epsilon ^3}{125}+\frac{21 \epsilon ^5}{15625}+\frac{78 \epsilon ^6}{78125}+\cdots$$
- Setting $\epsilon=1$ gives numerical value $0.75\cdots$
weak coupling approach
- use the similar idea to Feynman diagrams
- try $\epsilon x^5+ x=1$
- we get
$$ x(\epsilon)=1-\epsilon +5 \epsilon ^2-35 \epsilon ^3+285 \epsilon ^4-2530 \epsilon ^5+23751 \epsilon ^6+\cdots $$
- can we get a meaningful number out of this?
- yes, for example, Pade summation can be used
books
- Bender, Carl M., and Steven A. Orszag. 1999. Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Methods and Perturbation Theory. Springer.