Study/Meaningless Doubt2015. 8. 26. 21:18

1. Vector Calculus 3대 공식

Cfdl=f(b)f(a)SFda=VFdτCFdl=S(×F)da

 

 


 

2. 변형하여 값이 Vector 공식 (for a constant vector c)

Vfdτ=Sfda

pf.

cSfda=S(fc)da=V(fc)dτ=V(fc)dτ=V[(f)c+fc]dτ=Vcfdτ=cVfdτ

 

V(×F)dτ=SF×da

pf.

c(SF×da)=da(c×SF)=S(c×F)da=V(c×F)dτ=V[(×c)Fc(×F)]dτ=Vc(×F)dτ=cV(×F)dτ

 

Sf×da=Cfdl

pf.

cCfdl=C(fc)dl=S[×(fc)]da=S[f×c+f×c]da=S(f×c)da=S(da×f)c=cSf×da

 


 

3. 추가 변형 f(A),f(×A),b(×A),fg을 넣어서 더 변형시킬 수 있다.

 


 

4. Vector Area

Def.

aSda

 

 

Thm.

Sda=0

 

Coro.

a=12Cr×dl

 

Thm.

C(cr)dl=a×c

pf.
C(cr)dl=S(cr)×da=Sc×da=a×c
Note:(cr)=c×(×r)+r×(×c)+(c)r+(r)c=c×(×r)+(c)r=(c)r=c

 

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