# Shared Flashcard Set

## Details

Formula for MV test
formulas for MV Calc test
33
Engineering
10/31/2012

Term
Definition
 ∇F = ‹df/dx, df/dy, df/dz›
Term
 tangent plane
Definition
 ∇F‹x0 , y0, z0›*‹x, y, z›=∇‹x0, y0, z0›*‹x0, y0, z0› OR Z=fx(x0,y0,)(x-x0)+fy(x0,y0)(y-y0)+z0
Term
 normal line
Definition
 ‹x,y,z›=‹x0,y0,z0›+t∇f(x0,y0,z0)
Term
 chain rule
Definition
 if z=f(x,y) dz/dt=dz/dx*dx/dt + dz/dy*dx/dt
Term
 implicit form is
Definition
 x+y+z=0
Term
 parametric form is
Definition
 x= ____ty= ____tz= ____t
Term
 vector form is
Definition
 ‹x,y,z>=‹x0,y0,z0›+t∇f‹x,y,z›
Term
 formula for optimization is
Definition
 H(x,y)=d^2f/(d^2x)*d^2f/(d^2y)-(d^2f/(dxdy))^2
Term
 if H(x0,y0)<0
Definition
Term
 if H(x0,y0)>0
Definition
 if fxx(x0,y0)>0 minif fxx(x0,y0)<0 max
Term
 x^2+y^2 in polar form is
Definition
 r^2
Term
 x in polar form is
Definition
 rcosɵ
Term
 y in polar form is
Definition
 rsinɵ
Term
 Critical points are
Definition
 when df/dx = 0or df/dy = 0
Term
 Directional Derivative
Definition
 (gradient of equation) . (unit vector) ∇f(x) . ( V/|V| )
Term
 find the normal line using three points on a plane
Definition
 (p1-p2) x (p1-p3)
Term
 Acceleration Normal
Definition
 an = |v x a|/|v| (note: all are vectors)
Term
 Acceleration Tangential
Definition
 at=a(t) . (Ṽ/|v|) OR (v . A)/|v|
Term
 Area of a triangle from 3 points
Definition
 (AB . AC)/2   AB being the vector created by A-B AC being the vector created by A-C
Term
 Volume of a parallelopiped from three vectors
Definition
 A . ( B x C )
Term
 z in cylindrical coordinates is
Definition
 z
Term
 x in cylindrical coordinates is
Definition
 rcosɵ
Term
 y in cylindrical coordinates is
Definition
 rsinɵ
Term
 x^2 + y^2 in cylindrical coordinates is
Definition
 r^2
Term
 z in spherical coordinates is
Definition
 ρcosɸ
Term
 x in spherical coordinates is
Definition
 ρsinɸcosɵ
Term
 y in spherical coordinates is
Definition
 ρsinɸsinɵ
Term
 r in spherical coordinates is
Definition
 ρsinɸ
Term
 volume in spherical coordinates is
Definition
 dV = ρ^2 sinɸ dρ dɵ
Term
 Volume in cylindrical coordinates is
Definition
 dV= r dr dɵ dz
Term
 Linearization
Definition
 L(x) = f(x0,y0) + fx(x0,y0)(x-x0)+fy(x0,y0)(y-y0)
Term
 dot product
Definition
 |A||B|cos(ɵ)
Term
 cross product
Definition
 ABsin(ɵ)N
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