This module provides a collection of functions for performing various calculus operations such as derivatives, integrals, and numerical methods for improving accuracy.
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.
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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.
Computes the definite integral of a function func over the interval [a, b]. Utilizes the integral function from the math-kit module.
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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.
Approximates the definite integral of a function func over the interval [a, b] using Simpson's rule, a numerical integration method.
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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.
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.
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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.
Import the module:
javascript import { highOrderDerivative, definiteIntegral, simpsonsRule, rombergsMethod } from 'advanced-calculus-toolkit';