<p> FD Deriv, Cumulative Integration </p>

0e071233-c682-4856-aa95-9b249947fbf3 22 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

a 0.65 : b 12 : c 5 : d 4 : 14 mat

x sol 1 - 21 - 2 - 22 mat 1512 - 22 mat 31 sys

Explain . . .

1. For this example, plot/solve on canvas is not robust.

It excludes discrete solutions on the demand range.

2. Alternately, Solve succeeds nicely, pretty quick.

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Setup to plot/solve on the canvas.
Some kind of "secret" from Originator x sol Y a b 2^* c d * Y * - (x^- 0 ≡ Y 1 roots :

x Sol Y a b 2^* c d * Y * - (x^- 0 ≡ Y 1 - 5 solve :

sanity 0.875 - Sol 1.5 Sol 21 mat 0.019 4.543 21 mat

λ 1 - x ≤ (x 1.5 ≤ (* :

x sol λ / 1 - 2 1 - 2 - 2 2 mat 1 5 1 2 - 2 2 mat 3 1 sys

data x 0.875 - 1.5 0.875 - 0.0125 + (range : i 1 x rows range sol i el x i el Sol vectorize : for x sol augment 31 line :

data data :

data <p> FD Deriv, Cumulative Integration </p>

Finite differences "FD" derivative of data set data D X data 1 col : Y data 2 col : n X rows : deriv 1 el 0 : deriv n el 0 : i 2 n 1 - (range deriv i el 0.5 Y i 1 + el Y i el - X i 1 + el X i el - / Y i el Y i 1 - el - X i el X i 1 - el - / + (* : for deriv 1 el deriv 2 el : deriv n el deriv deriv rows el : X deriv augment 91 line :

Finite differences cumulative integration data Σ vx data 1 col : vy data 2 col : Y 1 el 0 : i 2 vx rows range Δx i el vx i el vx i 1 - el - : Y i el Y i 1 - el 12 / vy i 1 - el vy i el + (Δx i el * (* + : 21 line for vx Y augment 51 line :

Discrete FD derivative

data D

Discrete FD cumulative intgr'n

data Σ

data Σ data rows row 32 / 5.875 12 mat