Lapla

Symbolic Differentiation & Laplace Transform Utility for JavaScript
A scientific library delivering transparent, step-by-step symbolic computations for time-domain functions and their Laplace transforms.

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Overview

Lapla provides:

1. Expression parsing of any (f(t)) via string input.
2. Symbolic differentiation up to integer order (n), with each intermediate step logged.
3. Laplace transform $$(\mathcal{L}{,\cdot,}(s))$$ of the base function or its derivatives.
4. A CLI tool laplaceop and a programmatic LaplaceOperator class.

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Installation

npm install -g @galihru/lapla

Or to include locally in a project:

npm install @galihru/lapla

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Programmatic API

const { LaplaceOperator } = require('galihridhoutomo/Lapla');

// 1. Instantiate with a time-domain function f(t)
const op = new LaplaceOperator("exp(-3*t) + t^2");

// 2. First derivative:
//    d/dt [ e^{-3t} + t^2 ] = -3 e^{-3t} + 2 t
op.derivative(1);

// 3. Second derivative:
op.derivative(2);

// 4. Laplace transform of f(t):
//    L{e^{-3t} + t^2}(s) = 1/(s+3) + 2/s^3
op.laplace();

// 5. Laplace transform of the first derivative:
op.laplaceOfDerivative(1);

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CLI Usage

Once installed globally:

laplaceop "t^3*exp(-4*t)" -d 1 -l

Flags:

• -d, --deriv N : compute the $N$th derivative of $f(t)$
• -l, --laplace : compute the Laplace transform

Output is printed in clear, stepwise form.

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Mathematical Basis

• Differentiation:

  $$\frac{d^n}{dt^n}f(t) \quad\text{via symbolic engine.}$$

• Laplace Transform:

  $$\mathcal{L}{f(t)}(s) ;=; \int_{0^-}^{\infty} e^{-s t},f(t),\mathrm{d}t$$

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Testing

npm test

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License

MIT © 2025