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35 Cards in this Set
- Front
- Back
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Polar Coordinates - Cartesian Coordinates |
(rcos, rsin) |
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Work = |
Force o Distance |
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Force o Distance = |
lFl lDl cos |
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Volume of Parallelpiped |
la o (bxc)l |
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Cross Product of two line segments on a plane = |
normal to the plane |
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Area of a Parallelogram = |
llPQ x prll |
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Angle between two planes |
cos = ln1 o n2l --------------- lln1ll lln2ll |
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the direction vector perpendicular to a plane |
normal to the plane |
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normal = |
n1 x n2 |
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How do you find the intersection of two paths? |
Substitute "t" for "s" in one quation and set them equal |
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Two planes are perpendicular if .... |
the dot product of their normals equal 0
n1 o n2 = 0 |
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la x bl = |
lal lbl sin |
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a o b = |
lal lbl cos |
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Tangent vectors are |
the derivatives |
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(r, theta, z) --> cartesian coordinates = |
(rcos, rsin, z) |
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(x, y, z) ---> cylindrical coordinates = |
(sq root (x^2 +y^2), tan= y/x, z) |
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(p, theta, phi) ---->cartesian |
(psin(phi)cos(theta), psin(phi)sin(theta), pcos(phi)) |
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Spherical p^2 = |
x^2 + y^2 + z^2 |
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Distance between a plane and a line |
D = lax + by + cz + dl --------------------------- sq root (a^2 + b^2 + c^2) |
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proj b onto a = |
a o b ------- o a llall^2 |
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Arc Length |
S= Antideriv 0-t of the length of r'(u) du |
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DuF |
Gradient F O U |
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Maximum Value in the direction of |
the length of the gradient |
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Tan plane to surface |
Fx(x, y, z)(x-a) + Fy(x, y, z)(y-b) + Fz(x, y, z)(z-c) = 0 |
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V0 = |
(rcos, rsin) |
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V(t) = |
V0 + Antideriv 0-t of a(u) du |
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at = |
ll(v o a) / v ll
v' |
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an = |
ll (v x a) / v ll
kv^2 |
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k = |
ll (v x a) / v^3 ll |
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How to draw a gradient |
Draw a vector perpendicular to the tan plane to the surface |
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Which gradient is larger? |
ll Gradient F ll |
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Spherical coordinates |
(p, theta, phi) |
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Cylindrical coordinates |
(r, theta, z) |
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Polar |
(r, theta) |
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Implicit Function Theorem |
Dz/Dx = -Fx / Fz |
