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Calculus III: Section 13.4
Calculus III: Section 13.4 Professor Ensley Ship Math September 30, 2011 Professor Ensley (Ship Math) Calculus III: Section 13.4 September 30, 2011 1/6 Curvature Curvature Professor Ensley (Ship Math) Calculus III: Section 13.4 September 30, 2011 2/6 Curvature Curvature Professor Ensley (Ship Math) Calculus III: Section 13.4 September 30, 2011 2/6 Curvature Curvature Example. Find the curvature of the circle with vector parameterization r(s) = hcos (s/R), sin (s/R)i. Professor Ensley (Ship Math) Calculus III: Section 13.4 September 30, 2011 2/6 Curvature Curvature Professor Ensley (Ship Math) Calculus III: Section 13.4 September 30, 2011 2/6 Curvature Curvature Use ParametricPlot3D to visualize. Professor Ensley (Ship Math) Calculus III: Section 13.4 September 30, 2011 3/6 Curvature Curvature Professor Ensley (Ship Math) Calculus III: Section 13.4 September 30, 2011 3/6 Unit normal vector Unit normal vector Professor Ensley (Ship Math) Calculus III: Section 13.4 September 30, 2011 4/6 Unit normal vector Unit normal vector this Professor Ensley (Ship Math) Calculus III: Section 13.4 September 30, 2011 4/6 Osculating circles Osculating circles Professor Ensley (Ship Math) Calculus III: Section 13.4 September 30, 2011 5/6 Osculating circles Osculating circles Professor Ensley (Ship Math) Calculus III: Section 13.4 September 30, 2011 5/6 Osculating circles Osculating circles Professor Ensley (Ship Math) Calculus III: Section 13.4 September 30, 2011 5/6 Osculating circles Osculating circles in 3D Professor Ensley (Ship Math) Calculus III: Section 13.4 September 30, 2011 6/6
