Set: Calculus: Vector-Valued Functions

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All 14 Terms

Term Definition
vector valued function <r(t)> = <f(t),g(t),h(t)>
position function for a projectile <r(t)> = (v₀cosθ)t<i> + [h + (v₀sinθ)t - ½gt²]<j>
unit tangent vector <T(t)> = <r'(t)>/||<r'(t)>||
unit normal vector <N(t)> = <T'(t)>/||<T'(t)>||
tangential component of acceleration D[||<v>||] = <a> ⋅<T> = <v> ⋅<a>/||<v>||
normal component of acceleration ||<v>||*||<T'>|| = <a>⋅<N> = ||<v> x <a> ||/||<v>||
arc length function s = ∫√[x'(t)]² + [y'(t)]² + [z'(t)]²) dt = ∫||<r'(t)>||dt
arc length function s(u) = ∫√[x'(u)]² + [y'(u)]² + [z'(u)]²) du = ∫||<r'(u)>||du
derivative of arc length function ds/dt = ||<r'(t)>||
arc length parameter ||<r'(t)>|| = s
curvature K = ||d<T>/ds|| = ||<T'(s)>||
curvature for parameter t K = ||<T'(t)>||/||r'(t)|| = ||<r'(t)> x <r"(t)>||/||r'(t)||³
curvature in rectangular coordinates K = |y"|/[1+(y')²]^(3/2)
acceleration in terms of curvature <a(t)> = (d²s/dt²)<T> + K(ds/dt)²<N>

Set Information

Terms 14
Creator jtwilliams00
Created October 27, 2008
Groups None
Subjects mathematics, calculus, vector valued functions
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Most Missed Words

  1. position function for a projectile → <r(t)> = (v₀cosθ)t<i> + [h + (v₀sinθ)t - ½gt²]<j> - 5 misses
  2. arc length function → s = ∫√[x'(t)]² + [y'(t)]² + [z'(t)]²) dt = ∫||<r'(t)>||dt - 5 misses
  3. acceleration in terms of curvature → <a(t)> = (d²s/dt²)<T> + K(ds/dt)²<N> - 4 misses
  4. arc length function → s(u) = ∫√[x'(u)]² + [y'(u)]² + [z'(u)]²) du = ∫||<r'(u)>||du - 3 misses
  5. tangential component of acceleration → D[||<v>||] = <a> ⋅<T> = <v> ⋅<a>/||<v>|| - 2 misses
  6. unit normal vector → <N(t)> = <T'(t)>/||<T'(t)>|| - 2 misses
  7. curvature for parameter t → K = ||<T'(t)>||/||r'(t)|| = ||<r'(t)> x <r"(t)>||/||r'(t)||³ - 2 misses