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@jgphilpott
Last active November 19, 2022 08:24
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A collection of functions for performing differential and integral calculus in JavaScript.
# 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
// 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);
};
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