. p.1/11
[ ] F(x,y,z) = (F 1 (x,y,z),f 2 (x,y,z),f 3 (x,y,z)) = F 1 i+f 2 j+f 3 k div F = F 1 x + F 2 y + F 3 z F (divergence). p.1/11
[ ] F(x,y,z) = (F 1 (x,y,z),f 2 (x,y,z),f 3 (x,y,z)) = F 1 i+f 2 j+f 3 k div F = F 1 x + F 2 y + F 3 z F (divergence) = i x + j y + k z ( ) div F = F. p.1/11
. p.2/11
F. p.2/11
F (x,y,z) h. p.2/11
F (x,y,z) h h 2{ F(x + h,y,z) i + F(x h,y,z) ( i) 2 2 +F(x,y + h,z) j + F(x,y h,z) ( j) 2 2 +F(x,y,z + h) k + F(x,y,z h ) ( k) + ( )} 2 2. p.2/11
F (x,y,z) h h 2{ F(x + h,y,z) i + F(x h,y,z) ( i) 2 2 +F(x,y + h,z) j + F(x,y h,z) ( j) 2 2 +F(x,y,z + h) k + F(x,y,z h ) ( k) + ( )} 2 2 =h 2{( F 1 (x,y,z)+ hf 2 1x(x,y,z) ) ( F 1 (x,y,z)+( h)f 2 1x(x,y,z) ) + ( F 2 (x,y,z)+ hf 2 2y(x,y,z) ) ( F 2 (x,y,z)+( h)f 2 2y(x,y,z) ) + ( F 3 (x,y,z)+ hf 2 3z(x,y,z) ) ( F 3 (x,y,z)+( h)f 2 3z(x,y,z) )} +( ). p.2/11
F (x,y,z) h h 2{ F(x + h,y,z) i + F(x h,y,z) ( i) 2 2 +F(x,y + h,z) j + F(x,y h,z) ( j) 2 2 +F(x,y,z + h) k + F(x,y,z h ) ( k) + ( )} 2 2 =h 2{( F 1 (x,y,z)+ hf 2 1x(x,y,z) ) ( F 1 (x,y,z)+( h)f 2 1x(x,y,z) ) + ( F 2 (x,y,z)+ hf 2 2y(x,y,z) ) ( F 2 (x,y,z)+( h)f 2 2y(x,y,z) ) + ( F 3 (x,y,z)+ hf 2 3z(x,y,z) ) ( F 3 (x,y,z)+( h)f 2 3z(x,y,z) )} +( ) = h 3 div F+( ). p.2/11
h 3 h 0. p.3/11
h 3 h 0 (x,y,z). p.3/11
h 3 h 0 (x,y,z) div F(x,y,z). p.3/11
h 3 h 0 (x,y,z) div F(x,y,z) [ ]. p.3/11
h 3 h 0 (x,y,z) div F(x,y,z) [ ]. p.4/11
h 3 h 0 (x,y,z) div F(x,y,z) [ ] ρ(x,y,z) E(x,y,z) E = 1 ε 0 ρ ε 0 ( ). p.4/11
[ ] f(x,y,z) f = div (grad f) = ( f). p.5/11
[ ] f(x,y,z) f = div (grad f) = ( f) = 2 x + 2 2 y + 2 2 z (Laplacian) 2. p.5/11
[ ] f(x,y,z) f = div (grad f) = ( f) = 2 x + 2 2 y + 2 2 z (Laplacian) 2 [ ]. p.5/11
[ ] f(x,y,z) f = div (grad f) = ( f) = 2 x + 2 2 y + 2 2 z (Laplacian) 2 [ ] T(x,y,z). p.5/11
[ ] f(x,y,z) f = div (grad f) = ( f) = 2 x + 2 2 y + 2 2 z (Laplacian) 2 [ ] T(x,y,z). p.5/11
[ ] f(x,y,z) f = div (grad f) = ( f) = 2 x + 2 2 y + 2 2 z (Laplacian) 2 [ ] T(x,y,z) h = κ grad T ( κ ). p.5/11
[ ] f(x,y,z) f = div (grad f) = ( f) = 2 x + 2 2 y + 2 2 z (Laplacian) 2 [ ] T(x,y,z) h = κ grad T ( κ ) div( κ grad T) = κ T ( +κ T). p.5/11
[ ] f(x,y,z) f = div (grad f) = ( f) = 2 x + 2 2 y + 2 2 z (Laplacian) 2 [ ] T(x,y,z) h = κ grad T ( κ ) div( κ grad T) = κ T ( +κ T) ( ) T t = κ T. p.5/11
[ ] ( F F (rotation) F3 rot F = y F 2 F 1 z, z F 3 F 2 x, x F ) 1 = F y. p.6/11
[ ] ( F F (rotation) F3 rot F = y F 2 F 1 z, z F 3 F 2 x, x F ) 1 = F y. p.6/11
[ ] ( F F (rotation) F3 rot F = y F 2 F 1 z, z F 3 F 2 x, x F ) 1 = F y z y-z (x,y,z) h. p.6/11
[ ] ( F F (rotation) F3 rot F = y F 2 F 1 z, z F 3 F 2 x, x F ) 1 = F y z y-z (x,y,z) h z h { F 2 (x+ h,y,z) F 2 2(x h,y,z) F 2 1(x,y+ h,z)+f 2 1(x,y h,z)} +( ) 2. p.6/11
[ ] ( F F (rotation) F3 rot F = y F 2 F 1 z, z F 3 F 2 x, x F ) 1 = F y z y-z (x,y,z) h z h { F 2 (x+ h,y,z) F 2 2(x h,y,z) F 2 1(x,y+ h,z)+f 2 1(x,y h,z)} +( ) 2 =h {( F 2 (x,y,z)+ hf 2 2x(x,y,z) ) ( F 2 (x,y,z)+( h)f 2 2x(x,y,z) )} h {( F 1 (x,y,z)+ hf 2 1y(x,y,z) ) ( F 1 (x,y,z)+( h)f 2 1y(x,y,z) )} +( ). p.6/11
[ ] ( F F (rotation) F3 rot F = y F 2 F 1 z, z F 3 F 2 x, x F ) 1 = F y z y-z (x,y,z) h z h { F 2 (x+ h,y,z) F 2 2(x h,y,z) F 2 1(x,y+ h,z)+f 2 1(x,y h,z)} +( ) 2 =h {( F 2 (x,y,z)+ hf 2 2x(x,y,z) ) ( F 2 (x,y,z)+( h)f 2 2x(x,y,z) )} h {( F 1 (x,y,z)+ hf 2 1y(x,y,z) ) ( F 1 (x,y,z)+( h)f 2 1y(x,y,z) )} +( ) = h 2 {F 2x (x,y,z) F 1y (x,y,z)} +( ). p.6/11
h 2 h 0. p.7/11
h 2 h 0 (x,y,z) z- F 2 x F 1 y. p.7/11
h 2 h 0 (x,y,z) z- F 2 x F 1 y( F3 rot F = y F 2 F 1 z, z F 3 F 2 x, x F ) 1 y. p.7/11
h 2 h 0 (x,y,z) z- F 2 x F 1 y( F3 rot F = y F 2 F 1 z, z F 3 F 2 x, x F ) 1 y [ ]. p.7/11
h 2 h 0 (x,y,z) z- F 2 x F 1 y( F3 rot F = y F 2 F 1 z, z F 3 F 2 x, x F ) 1 y [ ]. p.8/11
h 2 h 0 (x,y,z) z- F 2 x F 1 y( F3 rot F = y F 2 F 1 z, z F 3 F 2 x, x F ) 1 y [ ] E = ρ ε 0, E = B t, B = 0, c2 B = E t + 1 ε 0 J E : B : J : ε 0 : c :. p.8/11
[ ]. p.9/11
[ ] F F = gradf f f F. p.10/11
[ ] F F = gradf f f F F F = rot f f f F. p.10/11
p.60 7 p.68 14. p.11/11