MATH-ANALYSIS

MATH-ANALYSIS can be used to perform various operations pertaining to mathematical analysis such as (symbolic) differentiation, (numeric and symbolic) integration etc.

Installation

$ npm install math-analysis

Usage

var ma = require('math-analysis');

ma exposes the following functions:

createFunction (fctSpec)

Creates a function (object) from the given string specification. The specification follows standard syntax, using the following built-in functions:

• sqrt(x): square root of x

• log(x): natural logarithm (basis e)

• exp(x): e to the power of x

• pow(x,y): x to the power of y

• sin(x): trigonometric function sine

• cos(x): trigonometric function cosine

• PI: constant π

Note: all built-in functions are computed through the respective function offered by Math, i.e. Math.sqrt, Math.log etc.

Example:

var f = ma.createFunction('2.1 * sqrt(x + 1/x)');

The function object created, henceforth denoted by f, has the following methods:

eval(x)

Returns the function value f(x) for the given x.

differentiate()

Returns a function (object) that represents the (symbolically) differentiated f or the derivative of f.

integral(a,b,s)

Computes the integral of f over the interval [a;b]. a and b must be provided and must be numbers. Otherwise the return value is undefined. The integral is computed as F(b) - F(a) for the antiderivative F of f if such an F can be determined (see integrate). Otherwise a numeric approximation of the integral is computed.

In the case of a numeric approach parameter s defines the number of sub-intervals into which [a;b] is "chopped" to approximate the integral. This parameter is an optional integer number not less than 1. If it is not supplied or invalid the default 1000 is used. The bigger the value of s the more accurate the approximation. It will nonetheless remain an approximation. So there is no guarantee that the approximation and the exact value will be the same.

Note that the value of the approximation will be undefined if NaN was encountered when computing the approximation. Keep in mind, however, that the existence of an x in [a;b] for which the function is undefined does not necessarily mean that NaN is indeed encountered. Depending on a and parameter s such an x may be "skipped".

integrate()

Returns the antiderivative of f (as a function). Computation of an antiderivative may not always succeed. If it fails the return value is undefined, which does not necessarily mean that there is no (known) antiderivative. The procedure for computing the antiderivative implemented here has limitations that will be lifted to a certain extent with future versions, but will (or can) never be fully removed. (See also integral).

rewrite()

Returns a function that is a simplified version of f. For instance, x + 0 becomes x and (1+2)*x - x becomes 2 * x etc. Note that rewriting may modify f. That is, rewriting does not return a rewritten copy of f, but rather operates on f itself. Thus, the return value can be ignored as it is merely a pointer to f itself that may come in handy for method-chaining. Hence it is always true that f === f.rewrite().

If for some reason you want to retain f as it was before rewriting simply store its string representation and, if required, apply ma.createFunction to the string to obtain a function object again.

Example

var f = ma.createFunction('x + 0');
var s1 = f.toString();
f.rewrite();
var s2 = f.toString();

Having executed the above code the two string variables s1 and s2 hold the strings 'x + 0' and 'x', respectively.

toString()

Returns the string representation of the function.

lookupTable (fct, from, to, step)

Creates a look-up table for the given function fct with values for x ranging from from to to using the given step size step. fct must have been created with createFunction. The other three parameters are also mandatory and must be of type number. Furthermore, step must be greater than 0 and from must not be greater than to. If any of these prerequisites are not met the return value of this function is undefined.

Example:

var f = ma.createFunction('2*x+1');
var t = ma.lookupTable(f,-1,2.1,0.5);

As a result t is [{x:-1,y:-1},{x:-0.5,y:0},{x:0,y:1},{x:0.5,y:2},{x:1,y:3},{x:1.5,y:4},{x:2,y:5}].