mes 3Speak Podcast

Definition of Derivative for Vector Functions

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https://3speak.tv/watch?v=mes/jfezftxf
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: https://inleo.io/threads/view/mes/re-leothreads-2nrv5yzqc
    • Sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FgQ3jBd9IFaWOakOWbHous
    • Notes: https://peakd.com/hive-128780/@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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      mes 3Speak PodcastBy Math Easy Solutions