A collection of functions for performing differential and integral calculus in JavaScript.

calculus.coffee

# Find the tangent of any polynomial function at x.
findTangent = (x, coefficients) ->

    slope = 0
    intercept = coefficients[0]

    for index in [1 ... coefficients.length]

        slope += coefficients[index] * index * Math.pow x, index - 1
        intercept += coefficients[index] * Math.pow x, index

    return [intercept - slope * x, slope]

# Find the area under any polynomial function within bounds.
# This function works assuming your curve is either entirely above or entirely below the x axis.
# If your curve crosses the x axis within the given bounds you will need to first find the roots (x intercepts) and then calculate the segments above and below the axis separately.
# For finding the roots of polynomials look here: https://gist.github.com/jgphilpott/e483b5fbe52a7233c292f35737e5a682
findArea = (lowerLimit, upperLimit, coefficients) ->

    lower = 0
    upper = 0

    for coefficient, index in coefficients

        lower += (coefficient * Math.pow lowerLimit, index + 1) / (index + 1)
        upper += (coefficient * Math.pow upperLimit, index + 1) / (index + 1)

    return Math.abs upper - lower

calculus.js

// Generated by CoffeeScript 2.7.0

var findArea, findTangent;

// Find the tangent of any polynomial function at x.
findTangent = function(x, coefficients) {
  var i, index, intercept, ref, slope;
  slope = 0;
  intercept = coefficients[0];
  for (index = i = 1, ref = coefficients.length; (1 <= ref ? i < ref : i > ref); index = 1 <= ref ? ++i : --i) {
    slope += coefficients[index] * index * Math.pow(x, index - 1);
    intercept += coefficients[index] * Math.pow(x, index);
  }
  return [intercept - slope * x, slope];
};

// Find the area under any polynomial function within bounds.
// This function works assuming your curve is either entirely above or entirely below the x axis.
// If your curve crosses the x axis within the given bounds you will need to first find the roots (x intercepts) and then calculate the segments above and below the axis separately.
// For finding the roots of polynomials look here: https://gist.github.com/jgphilpott/e483b5fbe52a7233c292f35737e5a682
findArea = function(lowerLimit, upperLimit, coefficients) {
  var coefficient, i, index, len, lower, upper;
  lower = 0;
  upper = 0;
  for (index = i = 0, len = coefficients.length; i < len; index = ++i) {
    coefficient = coefficients[index];
    lower += (coefficient * Math.pow(lowerLimit, index + 1)) / (index + 1);
    upper += (coefficient * Math.pow(upperLimit, index + 1)) / (index + 1);
  }
  return Math.abs(upper - lower);
};