multivariate_calculus

Handles calculus of several variables in multidimensional space. It works with both TypeScript and JavaScript projects seamlessly.

Installation

If you wish to work with this library in the browser, you can download it from here.

To install globally on your computer:

npm install multivariate_calculus --global

If you instead want to use this package to build something of your own:

npm install multivariate_calculus --save

Usage

Once installed properly, you can say in TypeScript:

import { Matrix } from "multivariate_calculus"
const A = new Matrix(2, 3);   // [[0, 0, 0], [0, 0, 0]]

or in JavaScript:

const mcalc = require("multivariate_calculus");
const A = new mcalc.Matrix(2, 3);   // [[0, 0, 0], [0, 0, 0]]

One can create and work with variables just like one would do in pen and paper.

const x = Scalar.variable("x");

The code takes care that the same variable or constant object is not created twice, avoiding the problem of having multiple copies of the same variable lying around in memory. That is, after the previous line if we say

const x_ = Scalar.variable("x");

this does not create a new object with the same name as that of x. Instead, it will return the original object that was first created with the name "x". Essentially x and x_ are pointing to the same object in memory.

One may choose to work with more than one variable too. There is support for scalar algebra for any number of variables.

import { Scalar } from "multivariate_calculus"

const x = Scalar.variable("x");
const y = Scalar.variable("y");
const two = Scalar.constant(2);
const three = Scalar.constant(3);
const expr1 = x.add(two);
const expr2 = x.add(y);

const value1 = expr1.at(new Map([
    [x, three]
]));
const value2 = expr2.at(new Map([
    [y, two]
]));

console.log(value1);

Upon execution value1 should be a Scalar.Constant object with a constant value of 5. Interestingly, expr1 and value2 have the same value: a Scalar.Expression object representing x + 2.

Almost all common algebraic scalar operations have been implemented. File an issue if something has been missed and should be implemented right away.

Vector algebra has been added to the library. One can very simply create vector constants and vector variables.

const i = Vector.constant([1, 0, 0]);
const A = Vector.variable("A");
const z = i.add(A);

On execution z will be a vector Expression whose value will be the vector sum of A and i.

This is still a work in progress. A documentation page is coming soon. Work is being done on building the project to make it a useful tool for Physics and Mathematics.

Features implemented:

• Matrix operations
• Tensor operations
• A system of variables and constants for Scalar
• A system of variables and constants for Matrix
• A system of variables and constants for Vector
• A system of variables and constants for Tensor
• Algebra of Scalar variables
• Algebra of Matrix variables
• Algebra of Vector variables
• Algebra of Tensor variables
• Calculating limits of arbitrary expressions of multiple variables
• Evaluating partial derivatives
• Evaluating integral with respect to single variable
• Evaluating multiple integrals: line, surface, volume