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

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