c723bf62-5053-47c3-b08d-6e3b75289180 20 4 5 decimal

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

X 1 1.5 2 2.5 41 mat :

Y 1.3 3.1 5.2 0.8 41 mat :

D 1 el 0 : i 24 range D i el 2 Y i el Y i 1 - el - X i el X i 1 - el - / (* D i 1 - el - : for 21 line

D 0 7.2 1.2 18.8 - 41 mat

Quadratic components i 24 range f i 1 - el D i el 2 / t X i 1 - el - (2^X i el X i 1 - el - (/ * D i 1 - el 2 / t X i el - (2^X i el X i 1 - el - (/ * - Y i el + D i el 2 / X i el X i 1 - el - (* - : for t f f : 21 line

Quadratic-Derivative components i 24 range d i 1 - el D i el 2 / t X i 1 - el - (2^X i el X i 1 - el - (/ * D i 1 - el 2 / t X i el - (2^X i el X i 1 - el - (/ * - Y i el + D i el 2 / X i el X i 1 - el - (* - (t diff : for t D d : 21 line

Piecewise Quadratic t f 13721 - t + (2^* + 10 / 4933 - 2 t * + (2^242 - t + (2^* - (* + 10 / 47 - 42 - 472 - t + (2^* + (* + 35 - 2 t * + (2^* + 10 / - 31 mat

Piecewise Quadratic-Derivative t D 721 - t + (* 5 / 63142 - t + (* + (* 2 t * - (* 5 / - 2942 - t + (* 35 - 2 t * + (* + (* 5 / - 31 mat

data Σ Finite diff's Cumul Integration 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 61 line :

data Deriv data Derivative BackSubstitution 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 101 line :

# # cases

Sy . :

size 14 :

clr black :

t quad t f 1 el t X 2 el ≤ t f 2 el t X 3 el ≤ t f 3 el cases :

plotSample Sy size clr Sy size clr Sy size clr Sy size clr 43 mat :

Data X Y plotSample augment :

t quadDeriv t D 1 el t X 2 el ≤ t D 2 el t X 3 el ≤ t D 3 el cases :

Data 1 1.3 . 14 black 1.5 3.1 . 14 black 2 5.2 . 14 black 2.5 0.8 . 14 black 45 mat

U 1.25 :

Interpolate V U quad : 1.75

Plot Collectors

Piecewise joined Quadratic Spline

x quad x quadDeriv Data U V + 14 red 1 5 mat 4 1 sys

Deriv x f 1 el x diff x f 2 el x diff x f 3 el x diff Data 41 sys :

Fnct x f 1 el x f 2 el x f 3 el Data 41 sys :

Piecewise derivatives

Deriv

Quadratic arcs

Fnct

t Int t 8524 t 2^* + (* 5 / t 4933 - 2 t * + (2^242 - t + (2^* - (* + (* 5 / t 55 - 1882 - t + (2^* + 35 - 2 t * + (2^* + (* 5 / - 31 mat :

t quadInt t Int 1 el t X 2 el ≤ t Int 2 el t X 3 el ≤ t Int 3 el cases :

x quadInt

Fnct x 0 3.25 0.01 range : i 1 x rows range Fnct i el x i el quad : 11 line for x Fnct augment 31 line :

CWD C:\SmathFile CurrentDirectory :

Fnct CWD QuadInt wfile 1

rData CWD QuadInt rfile :

Smooth discrete cumulative integration

rData Σ

Smooth discrete discontinuous derivative

rData Deriv

Inconvenience wrt the UNofficial/OFFicial Smath releases

The "cases" comes with the UNofficial Smath release. The "OFFicial release" comes with the maple(,) but the UNofficial Smath release does not come with the maple(,) functionality. As it looks, something is not coherent or some missing link or illogical restriction. Though the Quadratic Spline has limited use because it is not analytical wrt derivative/integral, it is useful in Engineering applications. In that Smath work sheet, copy the Maple vector of functions, paste in blank sheet of "Smath OFFicial release" for the vector of integrals.

u Φ 13721 - x + (2^* + 10 / 4933 - 2 x * + (2^242 - x + (2^* - (* + 10 / 47 - 42 - 472 - x + (2^* + (* + 35 - 2 x * + (2^* + 10 / - 31 mat :

i 13 range M i el u Φ i el u x - x int maple : for x Int M : 21 line

Dead expansion form the "Smath UNofficial release" x Int 13721 - x + (2^* + 10 / u x - x int maple 4933 - 2 x * + (2^242 - x + (2^* - (* + 10 / u x - x int maple 47 - 42 - 472 - x + (2^* + (* + 35 - 2 x * + (2^* + 10 / - u x - x int maple 31 mat

Transited via the "OFFicial Smath release" 13721 - x + (2^* + 10 / u x - x int maple 4933 - 2 x * + (2^242 - x + (2^* - (* + 10 / u x - x int maple 47 - 42 - 472 - x + (2^* + (* + 35 - 2 x * + (2^* + 10 / - u x - x int maple 31 mat x 13721 - x + (2^* + (* 5 / x 4933 - 2 x * + (2^* + 722 - x + (2^* - (* 5 / x 55 - 1882 - x + (2^* + 35 - 2 x * + (2^* + (* 5 / - 31 mat ≡