연속 방정식

 

 

 

 

notation

• f

 

• current \(j(x)=(j_0(x),j_1(x),j_2(x),j_3(x))\) satisfies
  \(\partial^{\mu} J_{\mu}=0\)
  
• we get a conserved quantity
  \(G=\int_V J_0(x) \,d^3 x\)
  
• Lagrangian can be used to express the current density explicity

 

• current 
  \(j(x)=(j^0(x),j^1(x),j^2(x),j^3(x))\)
  \(j^{\mu}(x)= \frac{\partial \mathcal{L}}{\partial ( \partial_\mu \phi )}\left(\frac{\partial\alpha_{s}(\phi)}{\partial s} \right) \)
  

• obeys the continuity equation
  \(\partial_{\mu} J^{\mu}=\sum_{\mu=0}^{3}\frac{\partial j^{\mu}}{\partial x^{\mu}}=0\)
  
• \(j^{4}(x)\) density of some abstract fluid
• \(\mathbf{J}=(j_x,j_y,j_z)\) velocity of this abstract fluid at each space time point
• conserved charge
  \(Q(t)=\int_V J_0(x) \,d^3 x\)
  \(\frac{dQ}{dt}=0\)
   
  

 

역사

 

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

 

 

메모

http://www.rose-hulman.edu/~bryan/lottamath/cons2d2.pdf

 

http://www.rose-hulman.edu/~bryan/lottamath/

 

 

 

http://en.wikipedia.org/wiki/Volumetric_flow_rate

http://en.wikipedia.org/wiki/Mass_flow_rate

 

 

• Math Overflow http://mathoverflow.net/search?q=

 

 

관련된 항목들

• 맥스웰 방정식

 

 

수학용어번역

• 단어사전
  
  • http://translate.google.com/#en%7Cko%7C
  • http://ko.wiktionary.org/wiki/
• 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=
• 한국통계학회 통계학 용어 온라인 대조표
• 남·북한수학용어비교
• 대한수학회 수학용어한글화 게시판

 

 

매스매티카 파일 및 계산 리소스

•  
• http://www.wolframalpha.com/input/?i=
• http://functions.wolfram.com/
• NIST Digital Library of Mathematical Functions
• Abramowitz and Stegun Handbook of mathematical functions
• The On-Line Encyclopedia of Integer Sequences
• Numbers, constants and computation
• 매스매티카 파일 목록

 

 

사전 형태의 자료

• http://ko.wikipedia.org/wiki/
• http://en.wikipedia.org/wiki/
• The Online Encyclopaedia of Mathematics
• NIST Digital Library of Mathematical Functions
• The World of Mathematical Equations

 

 

 

 

 

관련논문

• http://www.jstor.org/action/doBasicSearch?Query=
• http://www.ams.org/mathscinet
• http://dx.doi.org/

 

 

관련도서

• 도서내검색
  
  • http://books.google.com/books?q=
  • http://book.daum.net/search/contentSearch.do?query=