3bb344d3-ebf8-49aa-8ce2-dad7caf0b4b9 287 4 5 false false 0 decimal
&[DATE] &[TIME] - &[FILENAME]
&[PAGENUM] / &[COUNT]
 <content> <p>PLOT</p> </content> <content> <p>Utils</p> </content> unknown 1 <content> <p>pUtils</p> </content>

range utility

a b n pR a b a - n / 0 n range * + eval 1 1 line : <content> <p>pGrid</p> </content>

B# N# pGrid m kg s K A cd 1 6 mat 1 1 1 1 1 1 1 6 mat : B# rows 2 ≡ ( B# cols 2 ≡ ( & ( N# length 2 ≡ ( & X# Y# 1 2 mat B# 1 el B# 2 el N# 1 el pR eval B# 3 el B# 4 el N# 2 el pR eval 1 2 mat : X# Y# 1 2 mat B# N# 1 2 mat eval : if 2 1 line :

pGrid(F,U,V) returns a length(U)*lenght(V) matrix with [u,v,F(u,v)]

FS# U# V# pGrid m kg s K A cd 1 6 mat 1 1 1 1 1 1 1 6 mat : FS# IsMatrix FS# X# Y# 1 2 mat U# V# pGrid eval : r# 1 X# length range : c# 1 Y# length range : M# 0 : 1 3 mat FS# X# 1 el Y# 1 el feval IsMatrix M# r# c# el FS# X# r# el Y# c# el feval eval : M# r# c# el X# r# el Y# c# el FS# X# r# el Y# c# el feval eval 3 1 mat : if 3 1 line if 2 1 line :

FS# U# V# pGrid2 X# Y# 1 2 mat U# V# pGrid : X# Y# FS# X# Y# pGrid 1 3 mat eval 2 1 line : <content> <p>pQuiver</p> </content>

Quiver plot of f(x,y)≡[f.1(x,y) f.2(x,y)]

FS# U# V# pQuiver X# Y# F# 1 3 mat FS# U# V# pGrid2 : n# 1 X# length Y# length * ( range : r# 1 X# length range : c# 1 Y# length range : 1 2 mat Z# 0 : M# 0 : XY# 0 : 1 3 mat One# 1 pQuiver length 1 matrix + eval : Z# n# el t# F# n# el norme : ( 0 ≡ 0 0 stack eval F# n# el t# / eval if : sc# 0.9 Y# 2 el Y# 1 el - ( * Z# norme vectorize max / eval : XY# r# c# el X# r# el i Y# c# el * + eval : M# n# el sc# Z# n# el 1 el i Z# n# el 2 el * + ( * pQuiver * XY# n# el One# * + ReIm eval : 9 1 line :

Arrow ->

pQuiver 0 1 0.8 1 0.8 1 5 mat 0 0 0.08 0 0.08 - 1 5 mat i * + transpose eval :

Arrow -|>

pQuiver 0 1 0.8 1 0.8 0.8 1 6 mat 0 0 0.08 0 0.08 - 0.08 1 6 mat i * + transpose eval : <content> <p>pCMap</p> </content> <content> <p>pIPlot</p> </content>

Ber7 Cycle colors

 <content> <p>Examples</p> </content>

Vector Fields Quiver Examples

https://en.wikipedia.org/wiki/Integral_curve

Notation "Box":

Ingegral Curves & monochrome VF

 pIC

Map Colored Vector Field

 Q cm pXYLine vectorize 1 1 mat

"Range" Notation:

Ingegral Curves & monochrome VF

 pIC

Map Colored Vector Field

 Q cm pXYLine vectorize 1 1 mat

Potential and Gradient example

 Plot

Electric Field

Constant
Charges

Place Points

Box Plot

Steps

Plot

The integral curves (red) are the paths that positive test charges placed in the field would take, and they are collinear with the vector field (blue) and perpendicular to the potential contour lines (green).

Note: E isn't the field, it is divided by
it's norme for stabilizing the RK method