calculess v1.0.2

Calculess.js

A calculus library for javascript and NPM. Created by Blake Sanie.

Install

$ npm install calculess

Getting Started

Import package and create Calc object for future use

var Calculess = require('calculess');
var Calc = Calculess.prototype;

Documentation

Limits

Evaluate a limit

Calc.limAt( x , function );

Evaluate a limit from the left

Calc.limLeftOf( x , function );

Evaluate a limit from the right

Calc.limRightOf( x , function );

Methods:

• Accept ±Infinity as x value (parameter)
• Can output ±Infinity
• Output NaN when the limit does not exist

Examples:

function recip(x) {
    return 1 / x;
}

Calc.limLeftOf(0, recip); // -Infinity
Calc.limRightOf(0, recip); // Infinity
Calc.limAt(0, recip); // NaN
Calc.limAt(1, recip); // 1

Derivatives

Evaluate f'(x)

• Note: If the given function is not continuous or differentiable at the target, NaN is returned

Calc.deriv( x , function );

Evaluate a derivative to the nth degree of x

• Note: as the degree increases, .nthDeriv() becomes less accurate. Also, continuity and differentiability are not checked.

Calc.nthDeriv( degree, x , function );

Examples:

function para(x) {
    return x * x;
}

Calc.deriv(3, para); // 6
Calc.nthDeriv(2, 3, para); // 2
Calc.nthDeriv(3, 3, para); // 0

function sharp(x) {
    return Math.abs(x);
}

Calc.deriv(1, sharp); // 1
Calc.nthDeriv(2, 1, para); // 0
Calc.deriv(0, sharp); // NaN

Integrals

Evaluate an integral using trapezoidal Riemann Sums

Calc.integral( start , end , function , numSubintervals );

Evaluate a function's average value

Calc.averageValue( start , end , function , numSubintervals );

Note: As the number of subintervals increases, .intregral() becomes more accurate, though more time is required for calculations

Examples

function sin(x) {
    return Math.sin(x);
}

Calc.integral(0, Math.PI, sin, 5); // 1.9337655980928052
Calc.integral(0, Math.PI, sin, 10); // 1.9835235375094546
Calc.integral(0, Math.PI, sin, 100); // 1.999835503887445
Calc.integral(0, Math.PI, sin, 1000); // 1.9999983550656886
Calc.integral(0, Math.PI, sin, 10000); // 1.999999983550358