2.3
Smooth parametrization
∇
∫
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Calculus III
Unit 1 · Multivariable and Vector Calculus Toolbox
1.1
Vectors in 2D
1.2
Vectors in 3D
1.3
Dot Product
1.4
Cross Product
1.5
Lines
1.6
Planes
1.7
Quadric Surfaces
1.8
Cylindrical & Spherical
Unit 2 · Vector Valued Functions
2.1
Space Curves
2.2
Vector Calculus
2.3
Arc Length
2.3
Smooth parametrization
2.3
Arc length
2.3
Arc length parameter
2.4
TNB Vectors
2.5
Curvature
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Calculus III
Section 2.3
2.3 Smooth: the velocity r′(t) never jumps and never vanishes
2.3
Smooth: the velocity r′(t) never jumps and never vanishes
Curve
ex2
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The integral adds the vectors r(t)Δt tip to tail
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Arc length adds up the speed ‖r′(t)‖