Calc I & II Review

# Calc I & II Review - the cross product of two vectors...

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The following is a partial list of facts assumed known in Math 2401; Math 1501 and 1502 are prerequisites for this course, so all material from those courses is assumed known in Math 2401. Trig Identities (1) sin 2 x + cos 2 x = 1 (2) sin 2 x = 2 sin x cos x (3) cos 2 x = cos 2 x - sin 2 x (1) and (3) combine to give sin 2 x = 1 2 - 1 2 cos 2 x cos 2 x = 1 2 + 1 2 cos 2 x Calculus Derivatives of all six trig functions, ln x , e x , tan - 1 x Integration by parts, u-substitution, products and powers of trig functions A conceptual understanding of Riemann integration is also useful Linear Algebra Dot Product - a.k.a scalar product - the dot product of two vectors is always a number (scalar) . ~u · ~u = || ~u || 2 ~u · ~v = 0 ~u ~v ~u · ~v = || ~u |||| ~v || cos θ Cross Product - a.k.a vector product -
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Unformatted text preview: the cross product of two vectors is always a vector . ~u × ~v = ± ± ± ± ± ± ˆ ı ˆ ˆ k u 1 u 2 u 3 v 1 v 2 v 3 ± ± ± ± ± ± = ± ± ± ± u 2 u 3 v 2 v 3 ± ± ± ± ˆ ı-± ± ± ± u 1 u 3 v 1 v 3 ± ± ± ± ˆ + ± ± ± ± u 1 u 2 v 1 v 2 ± ± ± ± ˆ k ~u × ~v =-~v × ~u ~u × ~v = 0 ⇔ ~u k ~v || ~u × ~v || = || ~u |||| ~v || cos θ The direction of ~u × ~v is perpendicular to both ~u and ~v , oriented according to the right-hand rule. The magnitude || ~u × ~v || is equal to the area of the parallelogram spanned by ~u and ~v . Equation for a plane: ~ N · ( ~ r-~ r ) = 0...
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