a7cd6bcc-ae0b-4d0d-8753-cecf8a537462 15 4 5 decimal

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

Setup the companion system

u F 595000003 / kg m s 2^* / * 11 x 2 / - (2^- (* 0 x < (x 2 < (& 595000003 / kg m s 2^* / * x 0 ≥ 0 cases :

z ∫ u F u 0 x int : x ∫ z ∫ : 21 line

1 ∫ 1.4875 107^* Pa *

Incremental analysis procedure

x f x F : (User function ≡

Algo style Memo formula of incremental analysis for this demo example h 0.0001 : (increment ≡ x h f D1 x 2 h * - f x 2 h * + f - 4 h * / - : (1rst Derivative ≡ x h f D2 x 2 h * + f - 16 x h + f * + 30 x f * - 16 x h - f * + x 2 h * - f - 12 h 2^* / : (2nd Derivative ≡ x h f h_int h x h + f x f - (* 2 x f * + (x * : (Integral Curve [antiderivative] ≡ x h f h_cumul 2 h x h + f x f - (* 2 x f * + (x 2^* (* : (Cumulative Integration ≡ 51 line

x Y 50000 Pa * : (solve in consistant unit system ≡

x Φ 0.0035 0.5 * x h f h_int * :

x Φ x Y 2 1 sys 0.0035 x ∫ * x Y 2 1 sys

2 Φ 1.3883 105^* Pa *

0.97 Φ 1 Φ 21 mat 49475.4625 kg m s 2^* / * 52062.5002 kg m s 2^* / * 21 mat

0.0035 x ∫ * x Y - 0 ≡ x 0.9 1 solve x Φ x Y - 0 ≡ x 0.9 1 solve 21 mat 0.9761 0.9761 21 mat

x f 0.0035 x ∫ * Pa / :

f L H N Inverse dx H L - N / : i 1 N range ω i el L dx - (dx i * + : for j 1 ω rows range sol j el x f ω j el - 0 ≡ x 0 2.05 solve eval : for ω sol augment 41 line :

Inv f 0 1.3883 105^* 50 Inverse :

Inv

50 pts recursive 12 min