hellfelix / number-diff

Overview

Number Diff - An all-purpose tool for calculus

Functions

Number Diff is built around a calculus-like function, that is, a function that takes an f64 as an argument, returning an f64 according to some specific rule. In the current state of the crate, functions are limited to ƒ: ℝ ⟶ ℝ (have a look at the supported functions for which functions can be used).
There are plans to expand to ƒ: ℂ ⟶ ℂ in the not so distant future.

Usage

Functions are represented by the Function struct. The Function struct can be created by either parsing a string or combining functions using standard operations. A Function instance can then be used with the call(x) method (or when using the nightly feature, Function instances can be called directly).

Check out some examples!

Supported functions

Function	Parsing Identifier	In-code Function
sin	"sin(_)"	sin()
cos	"cos(_)"	cos()
tan	"tan(_)"	tan()
sec	"sec(_)"	sec()
csc	"csc(_)"	csc()
cot	"cot(_)"	cot()
asin	"asin(_)"	asin()
acos	"acos(_)"	acos()
atan	"atan(_)"	atan()
sinh	"sinh(_)"	sinh()
cosh	"cosh(_)"	cosh()
tanh	"tanh(_)"	tanh()
natural log	"ln(_)"	ln()
absolute value	"abs(_)"	abs()
square root	"sqrt(_)"	sqrt()
factorial	"_!"	factorial()
addition	"_ + _ "	+
subtraction	"_ - _"	-
multiplication	"_ * _"	*
division	"_ / _"	/
contant	"1", "-12", "3.14", etc.	f64
independent variable	"x"	Function::default()

Note that "_" in the table above refers to any other function of the ones provided above. Note also that the operations (+, -, *, /) cannot be applied to each other. Attempting to apply an operation to another operation will make the parser return a Parsing Error.

Derivatives

All of the supported functions are smooth functions which in turn means that once initialized, a Function is guaranteed to be a smooth function and so are all of its derivatives.

Derivatives are calculated analytically. The provided derivative function will always be the the exact derivative of the original function (although not always in simplest form).

Note that in its current state, differentiating might in some rare cases return NaN for certain input values where simplification fails to avoid a division by zero.

Function instances can be differentiated using the differentiate() method or using the derivative_of() function.

Integrals

Integration is stable for the most part. With a standard precision of 1000, integration uses Simpson's rule in order to find an approximate value of the integral.

For usage examples, check out the integration documentation!

Note that while integrating over an interval (including the bounds of integration) inside of which the value of the specified function is undefined, the resulting value might be NaN.

Also, integrating over an interval (including the bounds of integration) inside of which the value of the specified function is infinit, the resulting value might be inf even though the integral should converge.

Series Expansions

See this article for an explanation of series expansions.

Current stability of series expansions

Expansion Technique	Stability	Usage
Taylor series	Stable ✅	get_taylor_expansion()
Maclaurin series	Stable ✅	get_maclaurin_expansion()
Fourier series	Unimplemented ❌	N/A

License

The crate is licensed under the Apache License 2.0. For full license description, check out the License document!