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12 Cards in this Set
- Front
- Back
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You want to approximate a point. What do you do?
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Linear approximations with the tangent plane
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You want to find the derivative of a function in a specific direction. What do you do?
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Use the gradient vector.
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You want to find the maximum change for a point on a surface. What do you do?
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Find the gradient vector.
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You want to find the max / min of a surface given a certain constraint. What do you do?
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Lagrange multipliers
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You want to determine whether a certain critical point is a max/min/saddle. What do you do?
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Use the hessian.
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What is the hessian?
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hessian = fxx fyy - (fxy)^2
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How would you confirm a max?
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hessian > 0
fxx < 0 |
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How would you confirm a min?
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hessian > 0
fxx > 0 |
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How would you confirm a saddle point?
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hessian < 0
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What if the hessian equals 0?
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You need to imagine the surface in a new way.
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What is dV when integrating with cylindrical coordinates?
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dV = r dz dr d(theta)
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What is dV when integrating with spherical coordinates?
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dV = p^2 sin(phi) dp d(phi) d(theta)
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