SimReal: Mathematics - Differentiation - Vector UiA Logo


[SimReal] [Library]
Vector Differentiation

This application visualizes the derivative of a vector.

By default we have a vector sliding on the graph of the function:
y = f(x) = 8-0.05(x-5)2
This curve is parameterized by the parameter t = 0.25x (can be changed).

We want to study the derivative dr/dt of the vector to the point A on the graph.
Mark the checkbox ΔrA to show the vector to point A
Mark the checkbox ΔrB to show the vector to point B
Mark the checkbox Δr to show the difference vector ΔrB - ΔrA
Mark the checkbox Δr/Δt to show the vector Δr divided by Δt
Mark the checkbox 'dr/dt' to show the derivative of the vector ΔrA

Use the scrollbar at the bottom of the simulation window
to move the point B closer and closer to point A.
Look how Dr/Dt comes closer and closer to the dr/dt.
Control objects  :
Scrollbar        : Move the point B on the graph
xA               : Left  endpoint A
xB               : Right endpoint B
Parameterization : Parameterization of the function
rA               : Show the vector to the point A
rB               : Show the vector to the point B
Δr               : Show the difference vector rB-rA
Δr/Δt            : Show the difference vector divided by Dt
dr/dt            : Show the derivative of the vector rA
Tangent          : Show the tangent line at point A
Point            : Show the end points A and B
Axis             : Show axis
Grid             : Show grid
Graph            : Show the graph of the function 
Formula          : Show the formula for derivate of the vector rA
Frm              : Show a part of the formula (together with simulation window)
Reset            : Reset the application

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