Unit 08: Arc Length and Curvature


unit 01
unit 02
unit 03
unit 04
unit 05
unit 06
unit 07
unit 08
unit 09
unit 10
unit 11
unit 12

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Week HW 1 Week HW 2 Week HW 3 Week HW 4 Week HW 5 Week HW 6 Review 1 [PDF] Review 2 [PDF] Review 3 [PDF] Abstracts [PDF] Brochure [PDF]
Here is the verification of the curvature formula done today: 
r[t_]:= {x[t], y[t], z[t]}; 
s[t_]:= Sqrt[r'[t].r'[t]];
T[t_]:= r'[t]/s[t];
kappa1[t_]:= Sqrt[T'[t].T'[t]]/s[t]
kappa2[t_]:= Sqrt[Cross[r'[t], r''[t]].Cross[r'[t], r''[t]]]/s[t]^3
Simplify[kappa1[t]^2 == kappa2[t]^2]