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