Important_math_knowledge - Important math knowledge 1...

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Important math knowledge 1. Solution to typical differential equations (1) ), ( ) ( x Q y x P y = + + = - c dx e x Q e y dx x P dx x P ) ( ) ( ) ( . (2) , 0 ' ' 2 = - x x ω . t t Be Ae x ω ω + = - ( ω > 0) (3) , 0 ' ' 2 = + x x ω ). cos( φ ω + = t A x ( ω > 0) 2 . Basic expansions ... ! 3 ! 2 ) 0 ( ) ( 3 0 3 3 2 0 2 2 0 + + + + = x dx f d x dx f d x dx df f x f (4) ... ! 7 ! 5 ! 3 sin 7 5 3 + - + - = θ θ θ θ θ (5) ... ! 6 ! 4 ! 2 1 cos 7 4 2 + - + - = θ θ θ θ (note: 180 1 π = o ) (6) ... 315 17 15 2 3 tan 7 5 3 + + + + = θ θ θ θ θ (| θ | < 2 π ) (7) ... ! 3 ! 2 1 3 2 + + + + = x x x e x (| x | < 1) (8) ... ! 3 ) 2 )( 1 ( ! 2 ) 1 ( 1 ) 1 ( 3 2 + - - ± - + ± = ± x n n n x n n x x n (| x | < 1) (9) ... 4 3 2 ) 1 ln( 4 3 2 x x x x x - + - = + (| x | < 1) (10) 1 cos sin 2 2 = + x x , 3 . Derivative Y = f [u (t)], , ' ' u f dt du du df dt dy × = × = (chain rule) (11) ), cos( )' (sin
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Unformatted text preview: / sec )' (tan 2 2 t t t = = , sin / csc )' tan ( 2 2 t t t c-=-= (13) , )' ( t t e e = , / 1 )' (ln t t = 4 . Integration (14) x dx = ∫ , (15) ax a axdx cos 1 sin-= ∫ , ax a axdx sin 1 cos = ∫ , ( a = constant) (16) x dx x ln 1 = ∫ , 1 1 1 + + = ∫ n n x n dx x . (n ≠- 1)...
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  • Winter '08
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