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Vcf i fbyj vzx cxg. Electromagnetic energy flow the rate at which energy flows through a surface S is GG given by P = ∫ S da ⋅ S Useful Math Cartesian Gradient ∇t = ∂ t xˆ ∂ t yˆ ∂ t zˆ ∂ x ∂ y ∂ z Divergence ∇ ⋅ v z G = ∂ vx ∂ vy ∂ v ∂ x ∂ y ∂ z G ∂ vy ∂ v Curl ∇ × v = (x x ∂ vz ∂ vy ) xˆ ( ∂ v ∂ vz ) yˆ ( − )zˆ ∂ y ∂ z ∂ z ∂ x ∂ x. F B Y j @ ~ b L ~ j L O Ɏc } O J b v ܂ 񂩁H t ̃N y œh G Ă I I W i } O J b v ȒP ɍ ܂ B \ ʂ̓I W i ̓h G ł I ʂ̓ b Z W I C { L b g ́A p } O J b v ɁA p N ŊG ` A d q W Łu M v 邾 ŁA I W i ̃} O J b v n L b g ł B A ΂ A ꂳ A ɁE E B ܂ ܂ E E ς ܂ E E E I ~ b L ~ j Stitch A nStitch X y V ܂̃v v Z X ܂ A J Ԃ A lj ĊG ` ł ܂ I H i q @ ɂ Ă ܂ B d q W A M. V Z x cx dx dV c dc Z x cx dx x Z dx c x c c c c y x V c Z h x cx i dx e c V c F x T Ax A X i j ij x i j i i F x k A X j kj x j i ik i k k n Ax A T x Since A is symmetric Ax x min F x T Ax c implies b y di eren tiating with resp ect to x k k n Ax x b x T Ax x T T o minim ize w e require d d Divide b y d or d CHAPTER Examples Notation Problems.

= abc a'1 = abc a' 210 (a) (a(bcd))' = a'(bcd)' = a'b'(cd)'=a'b'(c'd') = a'b'c' b'd' (b) (abcb(c'd'))' = (abc)'(b(c'd'))'=(a'b'c')(b'(c'd')'). Ý b >}{®I I >Ú zI © >wR} ~{wRyL > Lz b X $ X $ fz ~ >wRy ­j¥ $ #. If a^x=b b^y=c c^z=a Prove xyz=1 Please give the solution a x =b => x=log a b b y =c=> y=log b c c z =a=> z=log c a xyz=(log a blog b c)log c a =log.

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