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The Laplace solvers are sourced from advanced Engineering books, adapted around Smath/ Maple companions. 1. Sokolnikoff & Redheffer [Berkeley, UC]. 2. Mercier [Arts & Métiers, Angers]. 3. Institut Technique Professionnel [Paris].

In this Smath document, we will attempt to survive these solvers for Smath. Each solver is given under typical forcing function q(t), c/w their corresponding set of parameters. Each type solved is export formula for low level software: Excel, Pocket calculators... Observe the two types of Maple instructions.

Each solver type is accompanied with a typical set of forcing q(t) ... that can be any q(t) of your choice, providing it has a Laplace.

1rst Order Type 1

natural definition s F t 0 > assume s t invlaplace maple ≡

UnitStep 1 ≡ UnitLinear t ≡ UnitGrow d t * exp ω * ≡ UnitDecay d t * - exp ω * ≡ UnitSqrt t sqrt ≡ 51 line

1rst Order Type 2

local definition s F t 0 > assume s t invlaplace maple 11 line ≡

UnitStep 1 ≡ UnitLinear t ≡ UnitGrow d t * exp ω * ≡ UnitDecay d t * - exp ω * ≡ UnitSqrt t sqrt ≡ 51 line

2nd Order Type 3

UnitStep 1 ≡ UnitLinear t ≡ UnitGrow d t * exp ω * ≡ UnitDecay d t * - exp ω * ≡ Fails Dirac Integral t sqrt ≡ 51 line

local definition s F t 0 > assume s t invlaplace maple 11 line ≡