Calc III - Ch13 formulae

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Author:
Anonymous
ID:
235856
Filename:
Calc III - Ch13 formulae
Updated:
2013-09-19 18:27:01
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calc iii formula
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Description:
Given some things, calculate other things.
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  1. Arc length of a vector function <x(t), y(t), z(t)>
  2. Unit tangent vector T of r(t)
  3. Curvature given arc length parametrization and T
  4. How to relate arc length to r(t)
    ds/dt = ||r'(t)||
  5. Curvature given T and r(t)
  6. Curvature given only r(t)
  7. Curvature of a plane curve given y = f(x)
  8. Find given only r(t)
  9. Find N given B and T
    N = B x T
  10. How to find the normal plane
    Use T(t) as the normal and r(t) for a given point t on the curve
  11. How to find the osculating plane
    Use B(t) as the normal and r(t) for a given point t
  12. v(t) given r(t)
    v(t) = r'(t)
  13. a(t) given r(t)
    a(t) = r''(t) = v'(t)
  14. v given T
    V = vT = ||v||T
  15. Tangential component of acceleration given r(t) and T
    ||r'(t)||T = T
  16. normal component of acceleration given r(t)

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