Calculess.dart

A Dart port for calculus library in dart and NPM. Originally Created by Blake Sanie.

Getting Started

Import and initialize package

import 'package:calculess/calculess.dart';

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 double.nan when the limit does not exist

Examples:

 recip(x) => 1 / x;


Calc.limLeftOf(0, recip); // -double.infinity
Calc.limRightOf(0, recip); // double.infinity
Calc.limAt(0, recip); // double.nan
Calc.limAt(1, recip); // 1

Derivatives

Evaluate f'(x)

  • Note: If the given function is not continuous or differentiable at the target, double.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:

num para(x) => x * x;

Calc.deriv(2, para); // 4
Calc.nthDeriv(2, 2, para); // 2
Calc.nthDeriv(3, 2, para); // 0

num sharp(num x) => x.abs();

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

Integrals

Evaluate an integral using midpoint 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

import 'dart:math' as math;

double sin(x) => math.sin(x);

Calc.integral(0, Math.PI, sin, 10); // 2.0082484079079745
Calc.integral(0, Math.PI, sin, 100); // 2.000082249070989
Calc.integral(0, Math.PI, sin, 1000); // 2.000000822467294
Calc.integral(0, Math.PI, sin, 10000); // 2.000000008224376
Calc.integral(0, Math.PI, sin, 100000); // 2.000000000081865

Libraries

calculess