Plots  of  vector fields

Manipulate Vectors  and Matrices

Vectors are represented by lists of numbers or objects
The vector operations are defined

({1,3,2}.{5,6,7})  ({6,4,5} + {6,7,8})

x[t] =2  t
y[t] =2  t^2
z[t] = 0
f = {x[t],y[t],z[t]}
D[f,t]

Get f and df at a certain time t=10

Get the Inverse of a matrix

Inverse[{{1,2},{2,3}}]

Is that true? Test it

Eigenvalues

Eigenvalues[{{1,2},{2,3}}]

Plots

Load the corresponding AddOns

<<Graphics`PlotField3D`

Surface  Plot in 3 dimensions

Plot3D[x^2+y^2,{x,-3,3},{y,-3,3}]

f  = {x,-y}

VectorPlot[f,{x,-1,1},{y,-1,1}]

Needs["VectorFieldPlots`"];VectorPlot3D[(({x,y,z})/((x^2)+(x^3)+(z^3))),{x,0.001`,1},{y,0.001`,1},{z,1,3}]

?VectorPlot3D

Needs["VectorFieldPlots`"];VectorPlot3D[Evaluate[(∂_({{x,y,z}}))((x^2)+(y^2)+(z^2))],{x,-1,1},{y,-1,1},{z,-1,1}]