Advanced Calculus Toolkit

This module provides a collection of functions for performing various calculus operations such as derivatives, integrals, and numerical methods for improving accuracy.

Functions

highOrderDerivative(func, x, order, dx = 0.0001)

Calculates the high-order derivative of a given function func at point x up to the specified order. Uses a recursive approach by iteratively applying the derivative function from the math-kit module.

• func: Function - The function for which the derivative is calculated.
• x: Number - The point at which the derivative is evaluated.
• order: Number - The order of the derivative to be calculated.
• dx: Number - The small increment for calculating the derivative. Default value is 0.0001.

definiteIntegral(func, a, b, dx = 0.0001)

Computes the definite integral of a function func over the interval [a, b]. Utilizes the integral function from the math-kit module.

• func: Function - The function to be integrated.
• a: Number - The lower bound of the interval.
• b: Number - The upper bound of the interval.
• dx: Number - The small increment for calculating the integral. Default value is 0.0001.

simpsonsRule(func, a, b, n = 100)

Approximates the definite integral of a function func over the interval [a, b] using Simpson's rule, a numerical integration method.

• func: Function - The function to be integrated.
• a: Number - The lower bound of the interval.
• b: Number - The upper bound of the interval.
• n: Number - The number of subintervals. Must be even. Default value is 100.

rombergsMethod(func, a, b, maxIterations = 100, tolerance = 1e-6)

Computes the definite integral of a function func over the interval [a, b] using Romberg integration, a method for improving the accuracy of numerical integration.

• func: Function - The function to be integrated.
• a: Number - The lower bound of the interval.
• b: Number - The upper bound of the interval.
• maxIterations: Number - The maximum number of iterations for Romberg integration. Default value is 100.
• tolerance: Number - The tolerance level for convergence. Default value is 1e-6.

Usage

Import the module:

javascript import { highOrderDerivative, definiteIntegral, simpsonsRule, rombergsMethod } from 'advanced-calculus-toolkit';

Lisensi

MIT