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| ∇F = ‹df/dx, df/dy, df/dz› |
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| ∇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 |
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Definition
| ‹x,y,z›=‹x0,y0,z0›+t∇f(x0,y0,z0) |
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Definition
if z=f(x,y)
dz/dt=dz/dx*dx/dt + dz/dy*dx/dt |
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| ‹x,y,z>=‹x0,y0,z0›+t∇f‹x,y,z› |
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| formula for optimization is |
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Definition
| H(x,y)=d^2f/(d^2x)*d^2f/(d^2y)-(d^2f/(dxdy))^2 |
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Definition
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Definition
if fxx(x0,y0)>0 min
if fxx(x0,y0)<0 max |
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when df/dx = 0
or df/dy = 0 |
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(gradient of equation) . (unit vector)
∇f(x) . ( V/|V| ) |
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| find the normal line using three points on a plane |
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Definition
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Definition
| an = |v x a|/|v| (note: all are vectors) |
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at=a(t) . (Ṽ/|v|)
OR
(v . A)/|v| |
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| Area of a triangle from 3 points |
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Definition
(AB . AC)/2
AB being the vector created by A-B
AC being the vector created by A-C
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| Volume of a parallelopiped from three vectors |
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| z in cylindrical coordinates is |
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| x in cylindrical coordinates is |
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Definition
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| y in cylindrical coordinates is |
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Definition
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| x^2 + y^2 in cylindrical coordinates is |
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Definition
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| z in spherical coordinates is |
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| x in spherical coordinates is |
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| y in spherical coordinates is |
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| r in spherical coordinates is |
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| volume in spherical coordinates is |
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| Volume in cylindrical coordinates is |
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Definition
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Definition
| L(x) = f(x0,y0) + fx(x0,y0)(x-x0)+fy(x0,y0)(y-y0) |
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