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6 x( ) 2 x( ) x( ) = ( ) x = [ ( ) x ı x + ( ) y ( ) y ( ) z ı y + ( ) z ] T ı z 2 x ( ) = 2 ( ) x + 2 ( ) 2 y + 2 ( ) 2 z 2

7 2 E = 1 2 E c 2 t 2 s(x,t) 2 s x + 2 s 2 y + 2 s 2 z = 1 2 s 2 c 2 t 2 c E x = [x y z] T

8 s(x,t) s(x,t) = Ae j(ωt k xx kyy kzz) A kx ky kz ω 0

9 s(x,t) k 2 xs(x,t)+k 2 ys(x,t)+k 2 zs(x,t) = 1 c 2ω2 s(x,t) s(x,t) k x 2 +k y 2 +k z 2 = 1 c 2ω2

10 s(x,t) = Ae j(ωt k xx kyy kzz) x = [0 0 0] T s(0,t) = Ae jωt

11 s(x,t) = Ae j(ωt k xx kyy kzz) s(x,t) kxx+kyy +kzz = C C

12 k k = [kx ky kz] T s(x,t) = Ae j(ωt kt x) s(x,t) k

13 δx δt s(x,t) = s(x+δx,t+δt) Ae j(ωt kt x) = Ae j [ω(t+δt) k T (x+δx)] = ωδt k T δx = 0

14 k δx k T δx = k δx = ωδt = k δx k 2 = ω 2 /c 2 δx δt = ω k

15 T = 2π/ω λ δx = λ δt = T = 2π ω T = λ k ω 2π = λ = k k ω

16 s(x,t) = Ae j(ωt kt x) = Ae jω(t αt x) α = k/ω c = ω/ k α c

17 s(x,t) = s(t α T x) ω0 s(x,t) = s(t α T x) = n= Sne jnω 0(t α T x) Sn = 1 T T 0 s(u)e jnω 0u du

18 s(x,t) ω = nω0 k α = k/ω

19 s(x,t) = s(t α T x) = 1 2π S(ω)e jω(t αt x) dω S(ω) = s(u)e jωu du

it = α + β i + γ 1 t + γ 2 t + γ 3 t +λ 1 ( i ) + λ 2 ( i ) + λ 3 ( i ) +δx i + ϵ it, it i i t t t i λ 1 λ 3 t t t i = α + β i + δx i + ϵ i i i i 12 Harrison Cleveland McKinley Roosevelt 10 8 6

α α λ α = = λ λ α ψ = = α α α λ λ ψ α = + β = > θ θ β > β β θ θ θ β θ β γ θ β = γ θ > β > γ θ β γ = θ β = θ β = θ β = β θ = β β θ = = = β β θ = + α α α α α = = λ λ λ λ λ λ λ = λ λ α α α α λ ψ + α =

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