Definition of Derivative for Vector Functions

In this video I go over the definition of derivative for a vector function, which is very similar to the definition for real valued functions. The derivative of a vector function is defined as the limit as h approaches zero of the secant vector (difference of two vectors separated by incrementing the parameter t by h) divided h. As h approaches zero the secant vector approaches a vector that is parallel to the tangent vector to the curve. I illustrate this with an animation using GeoGebra. I also quickly define the unit tangent vector, which is just the tangent vector of length 1 (obtained by dividing the tangent vector by its magnitude).

#math #science #calculus #vectorfunctions #geogebra

Timestamps

• Introduction to Derivatives and Integrals of Vector Functions: 0:00
• Definition of Derivative of a Vector Function: 0:15
• Secant vector is the vector between the position vectors in the definition of derivative: 1:36
• Tangent vector is secant vector multiplied by 1/h as h approaches zero: 4:28
• GeoGebra animation of the secant line approaching the tangent line: https://www.geogebra.org/m/sVCRDDmA 7:17
• Unit Tangent Vector is the tangent vector divided by its magnitude: 10:16

Notes and playlists

• Summary: @mes/re-leothreads-2nrv5yzqc
• Sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FgQ3jBd9IFaWOakOWbHous
• Notes: @mes/hfsetrue
• PDF Notes: https://1drv.ms/b/c/88862ef47bcaf6cd/Ee2-BBUHljpLvHetNARBqOwBnpCCRj8EM48W0E4lk2-jWw
• Vector Functions playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FgQ3jBd9IFaWOakOWbHous .

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