Calculus Algorithms

This library includes various algorithms for calculus.

Currently it's in heavy development and only few are implemented.

Just wait many more algorithms are coming soon!

If you want, you can contribute too!

If you like this library don't forget to start the repository!

calculus-algorithms / Modules

calculus-algorithms

Table of contents

Modules

• differentiation

  • backwardDiff
  • centralDiff
  • differentiate
  • forwardDiff

• integration

  • simpsonOneThird
  • simpsonThreeEighth
  • trapezoidalRule

Module: differentiation

Functions

backwardDiff

▸ backwardDiff(fx, x, h?): number

Remarks

This is a numerical method.

Example

backwardDiff(Math.log, 7)

backwardDiff(func1, 3, 0.0001)

const func1 = (arg0: number): number => {
  return 1 / (1 + arg0 * arg0)
}

Parameters

| Name | Type | Default value | Description | | :--- | :----------------------------- | :------------ | :------------------------------------- | | fx | (arg0: number) => number | undefined | Function to differentiate. | | x | number | undefined | Differentiate at this given value. | | h | number | 0.0001 | Optional parameter - step size to use. |

Returns

number

differentiation of given function at given value.

Defined in

differentiation/backwardDividedDifference.ts:22

centralDiff

▸ centralDiff(fx, x, h?): number

Remarks

This is a numerical method.

Example

centralDiff(Math.log, 7)

centralDiff(func1, 3, 0.0001)

const func1 = (arg0: number): number => {
  return 1 / (1 + arg0 * arg0)
}

Parameters

| Name | Type | Default value | Description | | :--- | :----------------------------- | :------------ | :------------------------------------- | | fx | (arg0: number) => number | undefined | Function to differentiate. | | x | number | undefined | Differentiate at this given value. | | h | number | 0.0002 | Optional parameter - step size to use. |

Returns

number

differentiation of given function at given value.

Defined in

differentiation/centralDividedDifference.ts:22

differentiate

▸ differentiate(expression): string

Remarks

This is a not a numerical method.

Example

diff("4x^3 - 3x^1 + 2x^2")

Parameters

| Name | Type | Description | | :----------- | :------- | :--------------------------- | | expression | string | Expression to differentiate. |

Returns

string

differentiation of given expression.

Defined in

differentiation/differentiate.ts:48

forwardDiff

▸ forwardDiff(fx, x, h?): number

Remarks

This is a numerical method.

Example

forwardDiff(Math.log, 7)

forwardDiff(func1, 3, 0.0001)

const func1 = (arg0: number): number => {
  return 1 / (1 + arg0 * arg0)
}

Parameters

| Name | Type | Default value | Description | | :--- | :----------------------------- | :------------ | :------------------------------------- | | fx | (arg0: number) => number | undefined | Function to differentiate. | | x | number | undefined | Differentiate at this given value. | | h | number | 0.0001 | Optional parameter - step size to use. |

Returns

number

differentiation of given function at given value.

Defined in

differentiation/forwardDividedDifference.ts:22

Module: integration

Functions

simpsonOneThird

▸ simpsonOneThird(func, lowerLimit, upperLimit): number

Example

simpsonOneThird(Math.log, 4, 5.2)

simpsonOneThird(func1, 0, 1)

const func1 = (arg0: number): number => {
  return 1 / (1 + arg0 * arg0)
}

Parameters

| Name | Type | Description | | :----------- | :----------------------------- | :------------------------------- | | func | (arg0: number) => number | Function to integrate | | lowerLimit | number | Lower limit to integrate within. | | upperLimit | number | Upper limit to integrate within. |

Returns

number

integration of given function within given limits.

Defined in

integration/simpsonOneThird.ts:19

simpsonThreeEighth

▸ simpsonThreeEighth(func, lowerLimit, upperLimit): number

Example

simpsonThreeEighth(Math.log, 4, 5.2)

simpsonThreeEighth(func1, 0, 1)

const func1 = (arg0: number): number => {
  return 1 / (1 + arg0 * arg0)
}

Parameters

| Name | Type | Description | | :----------- | :----------------------------- | :------------------------------- | | func | (arg0: number) => number | Function to integrate | | lowerLimit | number | Lower limit to integrate within. | | upperLimit | number | Upper limit to integrate within. |

Returns

number

integration of given function within given limits.

Defined in

integration/simpsonThreeEighth.ts:19

trapezoidalRule

▸ trapezoidalRule(func, lowerLimit, upperLimit): number

Example

trapezoidalRule(Math.log, 4, 5.2)

trapezoidalRule(func1, 0, 1)

const func1 = (arg0: number): number => {
  return 1 / (1 + arg0 * arg0)
}

Parameters

| Name | Type | Description | | :----------- | :----------------------------- | :------------------------------- | | func | (arg0: number) => number | Function to integrate | | lowerLimit | number | Lower limit to integrate within. | | upperLimit | number | Upper limit to integrate within. |

Returns

number

integration of given function within given limits.

Defined in

integration/trapezoidal.ts:19