"에어리 (Airy) 함수와 미분방정식"의 두 판 사이의 차이

수학노트
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1번째 줄: 1번째 줄:
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<h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">이 항목의 수학노트 원문주소</h5>
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==개요==
  
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* <math>y'' - xy = 0</math>
  
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<math>\mathrm{Ai}(x) = \frac{1}{\pi} \int_0^\infty \cos
  
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<h5>개요</h5>
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\left(\tfrac13t^3 + xt\right)\, dt,</math>
  
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* <math>y'' - xy = 0</math>
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<math>\mathrm{Bi}(x) = \frac{1}{\pi} \int_0^\infty \left
  
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<math>\mathrm{Ai}(x) = \frac{1}{\pi} \int_0^\infty \cos\left(\tfrac13t^3 + xt\right)\, dt,</math>
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[\exp\left(-\tfrac13t^3 + xt\right) + \sin\left(\tfrac13t^3
  
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<math>\mathrm{Bi}(x) = \frac{1}{\pi} \int_0^\infty \left[\exp\left(-\tfrac13t^3 + xt\right) + \sin\left(\tfrac13t^3 + xt\right)\,\right]dt.,</math>
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+ xt\right)\,\right]dt.,</math>
  
 
http://www.wolframalpha.com/input/?i=Ai%28x%29
 
http://www.wolframalpha.com/input/?i=Ai%28x%29
  
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==근사공식==
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* [[안장점 근사]]<br><math>x>>0</math> 일 때,<br><math>
  
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\mathrm{Ai}(x) \sim \frac{e^{-\frac{2 x^{3/2}}{3}}}{2 \sqrt
  
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{\pi } \sqrt[4]{x}}</math><br><math>x<<0</math> 일
  
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때,<br><math>\mathrm{Ai}(x) \sim  \frac{\sin \left(\frac{2
  
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<h5 style="margin: 0px; line-height: 2em;">근사공식</h5>
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|x|^{3/2}}{3}+\frac{\pi }{4}\right)}{\sqrt{\pi } \sqrt[4]{|
  
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* [[안장점 근사]]<br><math>x>>0</math> 일 때,<br><math>\mathrm{Ai}(x) \sim \frac{e^{-\frac{2 x^{3/2}}{3}}}{2 \sqrt{\pi } \sqrt[4]{x}}</math><br><math>x<<0</math> 일 때,<br><math>\mathrm{Ai}(x) \sim  \frac{\sin \left(\frac{2 |x|^{3/2}}{3}+\frac{\pi }{4}\right)}{\sqrt{\pi } \sqrt[4]{|x|}}</math><br>
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x|}}</math><br>
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* [http://www.math.umn.edu/%7Eymori/docs/teaching/fall08/airy.pdf Asymptotics of the Airy Function]<br>
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* [http://www.math.umn.edu/
  
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%7Eymori/docs/teaching/fall08/airy.pdf Asymptotics of the
  
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Airy Function]<br>
  
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<h5>역사</h5>
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==역사==
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* http://www.google.com/search?hl=en&tbs=tl:1&q=
 
* http://www.google.com/search?hl=en&tbs=tl:1&q=
 
* [[수학사연표 (역사)|수학사연표]]
 
* [[수학사연표 (역사)|수학사연표]]
  
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<h5>메모</h5>
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==메모==
  
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* Math Overflow http://mathoverflow.net/search?q=
 
* Math Overflow http://mathoverflow.net/search?q=
  
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<h5>관련된 항목들</h5>
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==관련된 항목들==
  
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<h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">수학용어번역</h5>
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==수학용어번역==
  
 
*  단어사전<br>
 
*  단어사전<br>
69번째 줄: 83번째 줄:
 
** http://www.forvo.com/word/airy/#en
 
** http://www.forvo.com/word/airy/#en
 
** 아이어리?
 
** 아이어리?
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* [http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=&fstr= 대한수학회 수학 학술 용어집]<br>
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* [http://mathnet.kaist.ac.kr/mathnet/math_list.php?
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** http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=eng_term&fstr=
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* [http://www.nktech.net/science/term/term_l.jsp?l_mode=cate&s_code_cd=MA 남·북한수학용어비교]
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mode=list&ftype=&fstr= 대한수학회 수학 학술 용어집]<br>
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* [http://kms.or.kr/home/kor/board/bulletin_list_subject.asp?bulletinid=%7BD6048897-56F9-43D7-8BB6-50B362D1243A%7D&boardname=%BC%F6%C7%D0%BF%EB%BE%EE%C5%E4%B7%D0%B9%E6&globalmenu=7&localmenu=4 대한수학회 수학용어한글화 게시판]
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** http://mathnet.kaist.ac.kr/mathnet/math_list.php?
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mode=list&ftype=eng_term&fstr=
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* [http://www.nktech.net/science/term/term_l.jsp?
  
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l_mode=cate&s_code_cd=MA 남·북한수학용어비교]
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*
  
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[http://kms.or.kr/home/kor/board/bulletin_list_subject.asp?
  
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<h5>매스매티카 파일 및 계산 리소스</h5>
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bulletinid=%7BD6048897-56F9-43D7-8BB6-50B362D1243A
  
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* https://docs.google.com/file/d/0B8XXo8Tve1cxbl96STk2T3dpajg/edit
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%7D&boardname=%BC%F6%C7%D0%BF%EB%BE%EE
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%C5%E4%B7%D0%B9%E6&globalmenu=7&localmenu=4 대한수학회 수학
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용어한글화 게시판]
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==매스매티카 파일 및 계산 리소스==
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*  
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https://docs.google.com/file/d/0B8XXo8Tve1cxbl96STk2T3dpajg/
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edit
 
* http://www.wolframalpha.com/input/?i=
 
* http://www.wolframalpha.com/input/?i=
 
* http://functions.wolfram.com/
 
* http://functions.wolfram.com/
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* [http://dlmf.nist.gov/ NIST Digital Library of Mathematical Functions]
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* [http://dlmf.nist.gov/ NIST Digital Library of  
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* [http://people.math.sfu.ca/%7Ecbm/aands/toc.htm Abramowitz and Stegun Handbook of mathematical functions]
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* [http://www.research.att.com/%7Enjas/sequences/index.html The On-Line Encyclopedia of Integer Sequences]
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Mathematical Functions]
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* [http://numbers.computation.free.fr/Constants/constants.html Numbers, constants and computation]
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* [http://people.math.sfu.ca/%7Ecbm/aands/toc.htm Abramowitz  
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* [https://docs.google.com/open?id=0B8XXo8Tve1cxMWI0NzNjYWUtNmIwZi00YzhkLTkzNzQtMDMwYmVmYmIxNmIw 매스매티카 파일 목록]
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and Stegun Handbook of mathematical functions]
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* [http://www.research.att.com/%7Enjas/sequences/index.html  
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The On-Line Encyclopedia of Integer Sequences]
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*  
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[http://numbers.computation.free.fr/Constants/constants.html  
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Numbers, constants and computation]
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* [https://docs.google.com/open?
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id=0B8XXo8Tve1cxMWI0NzNjYWUtNmIwZi00YzhkLTkzNzQtMDMwYmVmYmIx
  
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NmIw 매스매티카 파일 목록]
  
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<h5>사전 형태의 자료</h5>
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==사전 형태의 자료==
  
 
* http://ko.wikipedia.org/wiki/
 
* http://ko.wikipedia.org/wiki/
 
* http://en.wikipedia.org/wiki/Airy_equation
 
* http://en.wikipedia.org/wiki/Airy_equation
 
* http://en.wikipedia.org/wiki/WKB_approximation
 
* http://en.wikipedia.org/wiki/WKB_approximation
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* [http://eom.springer.de/default.htm The Online Encyclopaedia of Mathematics]
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* [http://eom.springer.de/default.htm The Online  
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* [http://dlmf.nist.gov/ NIST Digital Library of Mathematical Functions]
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* [http://eqworld.ipmnet.ru/ The World of Mathematical Equations]
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Encyclopaedia of Mathematics]
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* [http://dlmf.nist.gov/ NIST Digital Library of  
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Mathematical Functions]
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* [http://eqworld.ipmnet.ru/ The World of Mathematical  
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Equations]
  
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<h5>리뷰논문, 에세이, 강의노트</h5>
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==리뷰논문, 에세이, 강의노트==
  
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<h5>관련논문</h5>
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==관련논문==
  
 
* http://www.jstor.org/action/doBasicSearch?Query=
 
* http://www.jstor.org/action/doBasicSearch?Query=
120번째 줄: 174번째 줄:
 
* http://dx.doi.org/
 
* http://dx.doi.org/
  
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<h5>관련도서</h5>
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==관련도서==
  
 
*  도서내검색<br>
 
*  도서내검색<br>
 
** http://books.google.com/books?q=
 
** http://books.google.com/books?q=
 
** http://book.daum.net/search/contentSearch.do?query=
 
** http://book.daum.net/search/contentSearch.do?query=

2012년 10월 21일 (일) 13:04 판

개요

  • \(y'' - xy = 0\)

\(\mathrm{Ai}(x) = \frac{1}{\pi} \int_0^\infty \cos \left(\tfrac13t^3 + xt\right)\, dt,\)

\(\mathrm{Bi}(x) = \frac{1}{\pi} \int_0^\infty \left [\exp\left(-\tfrac13t^3 + xt\right) + \sin\left(\tfrac13t^3 + xt\right)\,\right]dt.,\)

http://www.wolframalpha.com/input/?i=Ai%28x%29





근사공식

  • 안장점 근사
    \(x>>0\) 일 때,
    \( \mathrm{Ai}(x) \sim \frac{e^{-\frac{2 x^{3/2}}{3}}}{2 \sqrt {\pi } \sqrt[4]{x}}\)
    \(x<<0\) 일

때,
\(\mathrm{Ai}(x) \sim \frac{\sin \left(\frac{2 |x|^{3/2}}{3}+\frac{\pi }{4}\right)}{\sqrt{\pi } \sqrt[4]{| x|}}\)

%7Eymori/docs/teaching/fall08/airy.pdf Asymptotics of the

Airy Function]




역사



메모



관련된 항목들

수학용어번역

mode=list&ftype=&fstr= 대한수학회 수학 학술 용어집]

mode=list&ftype=eng_term&fstr=

l_mode=cate&s_code_cd=MA 남·북한수학용어비교]

[http://kms.or.kr/home/kor/board/bulletin_list_subject.asp?

bulletinid=%7BD6048897-56F9-43D7-8BB6-50B362D1243A

%7D&boardname=%BC%F6%C7%D0%BF%EB%BE%EE

%C5%E4%B7%D0%B9%E6&globalmenu=7&localmenu=4 대한수학회 수학

용어한글화 게시판]



매스매티카 파일 및 계산 리소스

https://docs.google.com/file/d/0B8XXo8Tve1cxbl96STk2T3dpajg/

edit

Mathematical Functions]

and Stegun Handbook of mathematical functions]

The On-Line Encyclopedia of Integer Sequences]

[http://numbers.computation.free.fr/Constants/constants.html

Numbers, constants and computation]

id=0B8XXo8Tve1cxMWI0NzNjYWUtNmIwZi00YzhkLTkzNzQtMDMwYmVmYmIx

NmIw 매스매티카 파일 목록]



사전 형태의 자료

Encyclopaedia of Mathematics]

Mathematical Functions]

Equations]



리뷰논문, 에세이, 강의노트

관련논문



관련도서

원본 주소 "https://wiki.mathnt.net/index.php?title=에어리_(Airy)_함수와_미분방정식&oldid=15058"