lecture13

lecture13 - 2006 Fall MATH 100 Lecture 13 1 ATH 100 Lecture...

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Unformatted text preview: 2006 Fall MATH 100 Lecture 13 1 ATH 100 Lecture 13 Midterm Review ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 1 1 2 2 2 1 2 2 1 2 2 cos , tan , : , , , , cos , sin sin , cos sin : , , , , cos , , sin : , , , , tan , , : , , , , , sin , cos : , , , , , tan , : , , , , conversion and system Coordinate (A) z y x z x y z y x z y x z y x z y x z r z r z r z r z r z z r y r x z y x z r z z x y y x r z r z y x + + = = + + = → = = = → = = = → = = + = → = = = → = = + = → − − − − φ θ ρ φ θ ρ φ ρ θ φ ρ θ φ ρ φ θ ρ φ ρ θ θ φ ρ θ φ θ ρ φ θ θ ρ φ θ ρ θ θ θ θ θ θ 2006 Fall MATH 100 Lecture 13 2 Ex: ( ) ( ) s coordinate spherical and l cylindrica to 1 , 2 , 2 Change − = x,y,z Sol: 5 1 cos , 4 , 5 1 2 2 1 , 4 2 2 tan , 2 2 2 1 1 2 2 − − = − = = + + = = − = − = = + = φ π θ ρ π θ z r (B) Quadric surfaces 2 2 2 = + + + + + + + + + J Iz Hy Gz Fyz Exz Dxy Cz By Ax ATH 100 Lecture 13 Midterm Review 2006 Fall MATH 100 Lecture 13 3 Canonical equations: paraboliod hyperbolic ...... paraboloid elliptic ...... cone elliptic ...... sheets two of d hyperboloi ...... 1 sheet one of d hyperboloi ...... 1 ellipsoid ...... 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 a x b y z b y a x z b y a x z c z b y a x c z b y a x c z b y a x − = + = + = − = − + = − + = + + ATH 100 Lecture 13 Midterm Review 2006 Fall MATH 100 Lecture 13 4 (C)Vector-valued functions Parametric equation: Derivative: ( ) ( ) ( ) ( ) ( ) ( ) ( ) t z t y t x k t z j t y i t x t r , , = + + = G G G G ( ) ( ) ( ) ( ) ( ) ( ) ( ) t z t y t x k t z j t y i t x t r...
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lecture13 - 2006 Fall MATH 100 Lecture 13 1 ATH 100 Lecture...

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