AI Math Handbook Calculator

- Computer Algebra System of Fractional Calculus

coding fill tangent polar coordinate zoom graph by mouse wheel

Button To do

Clear input

symbolic answer

JavaScript numeric answer

1st row algebra

simplify `sin^((0.5))(x)`

expand `(x-1)^2`

factor `(x^2-1)`

combine `(1-1/x)`

convert sin(x) to exp(x)

convert asin(x) to log(x)

convert exp(x) to sin(x)

convert sin(x) to sinh(x)

convert 2-i to complex() comvert 2-i to complex(2,-1)

inverse ( sin(x) )

2nd row calculus: default variable is x

convert sin(x) to integral definition

differentiate `d/dx sin(x)`

integrate ∫ sin(x) dx

infinite integration `int_0^oo ( exp(-x) ) dx`

nth derivative formula `d^n/dx^n sin(x)`

semiderivative `d^(0.5)/dx^(0.5) sin(x)`

semiintegrate `d^(-0.5)/dx^(-0.5) sin(x)`

ODE solve ordinary differential equation for y,
ODE( y'-y-x^x=0),

PDE solve partial differential equation for y,
PDE( ds(y,t)-ds(y,x)=0),

test solution for equation and diff equation

3th row discrete math: default index variable is k

convert sin(x) to series definition

Taylor series expansion taylor(sin(x))

series ( sin(x) )

difference Δ`k^2`

Indefinite sum ∑ 1/k^6

partial sum `sum_(k=0)^n` k

partial sum `sum_(k=1)^n` k

infinite sum sum( x^k/k! as k->oo )

infinite sum `sum_(k=1)^oo x^k/k`

laplace laplace(x) transform laplace(x)

fsolve solve functional equation for f(x) f(x+1)-f(x)=x

rsolve solve recurrence equation for y(x) y(x+1)-y(x)=x

4th row Numeric math

definition ( sinh(x) )

limit lim( sin(x)/x as x->0 )

limoo limit( log(x)/x as x->oo )

numeric limit `lim _(x->0) sin(x)/x`

numeric integrate `int _0^1` sin(x) dx

numeric sum `sum _(x=1)^8` x

numeric solve equation nsolve`( x^2-1=0 )`

solve equation for x, solve( exp(x)+exp(-x)=4 )

solver system of equations for x,y solver( exp(x)+exp(-x)==4 )

complex matrix calculator

numeric answer

5th row Interactive Plot: zoom by mouse wheel

plot sin(x) and `x^2`

parametric plot parametricplot( x=sin(t) , y=cos(2*t) )

contour contour(sin(x))

implicit plot `x^2+y^2=1 and x^2+y^2=4`

polar plot polarplot(sin(4*x))

overlap plot sin(x)

complex plot z complexplot(z)

6th row Interactive Plot 2D: zoom by mouse wheel

plot2D (sin(x)) show diff and integral curves

parametric curve in 2D

contour plane surface in 2D

diff2D (sin(x))

integrate2D (sin(x))

seimd2D (sin(x))

ode plot graphically solve y'=sin(x)

re2D(sqrt(x)) show 2 curves of real and imaginary in real variables

im2D(sqrt(x)) show 2 curves of real and imaginary in imag variables

7th row 2D + 3D Plot: zoom by mouse wheel

plot3D(sin(x))

parametric3D(t,t,t)

contour3D(x*y)

implicit3D(x*y*z-t)

wireframe3D(x*y) wireframe in 3D

parametric curve in 3D

complex3D(sqrt(x)) show complex function in complex variables

Show function graph. sin ?

AI chat GPT ??

8th row Interactive Plot 3D : zoom by mouse wheel

surface3D(x*y) surface in 3D

function3D(sin(x)) surface in 3D

section3D(x*y) in 4 graphs

spin3D(sin(x)) in 4 graphs

graph3D(x) in 10 styles

for equation, vector, point, parametric, vector field

data3D(x,y,z,c,t) 3D, 4D, 5D data in 10 styles

for explicit surface, polar explicit surface, implicit surface, line, parametric curve, parametric surface, point, vector, vector field, toggle switch, variable, function, variable slider

clear x

All Clear memory clear(0)

Button	To do
	Clear input
	symbolic answer
	JavaScript numeric answer
1st row	algebra
	simplify `sin^((0.5))(x)`
	expand `(x-1)^2`
	factor `(x^2-1)`
	combine `(1-1/x)`
	convert sin(x) to exp(x)
	convert asin(x) to log(x)
	convert exp(x) to sin(x)
	convert sin(x) to sinh(x)
	convert 2-i to complex() comvert 2-i to complex(2,-1)
	inverse ( sin(x) )
2nd row	calculus: default variable is x
	convert sin(x) to integral definition
	differentiate `d/dx sin(x)`
	integrate ∫ sin(x) dx
	infinite integration `int_0^oo ( exp(-x) ) dx`
	nth derivative formula `d^n/dx^n sin(x)`
	semiderivative `d^(0.5)/dx^(0.5) sin(x)`
	semiintegrate `d^(-0.5)/dx^(-0.5) sin(x)`
	ODE solve ordinary differential equation for y, ODE( y'-y-x^x=0),
	PDE solve partial differential equation for y, PDE( ds(y,t)-ds(y,x)=0),
	test solution for equation and diff equation
3th row	discrete math: default index variable is k
	convert sin(x) to series definition
	Taylor series expansion taylor(sin(x))
	series ( sin(x) )
	difference Δ`k^2`
	Indefinite sum ∑ 1/k^6
	partial sum `sum_(k=0)^n` k
	partial sum `sum_(k=1)^n` k
	infinite sum sum( x^k/k! as k->oo )
	infinite sum `sum_(k=1)^oo x^k/k`
	laplace laplace(x) transform laplace(x)
	fsolve solve functional equation for f(x) f(x+1)-f(x)=x
	rsolve solve recurrence equation for y(x) y(x+1)-y(x)=x
4th row	Numeric math
	definition ( sinh(x) )
	limit lim( sin(x)/x as x->0 )
	limoo limit( log(x)/x as x->oo )
	numeric limit `lim _(x->0) sin(x)/x`
	numeric integrate `int _0^1` sin(x) dx
	numeric sum `sum _(x=1)^8` x
	numeric solve equation nsolve`( x^2-1=0 )`
	solve equation for x, solve( exp(x)+exp(-x)=4 )
	solver system of equations for x,y solver( exp(x)+exp(-x)==4 )
	complex matrix calculator
	numeric answer
5th row	Interactive Plot: zoom by mouse wheel
	plot sin(x) and `x^2`
	parametric plot parametricplot( x=sin(t) , y=cos(2*t) )
	contour contour(sin(x))
	implicit plot `x^2+y^2=1 and x^2+y^2=4`
	polar plot polarplot(sin(4*x))
	overlap plot sin(x)
	complex plot z complexplot(z)
6th row	Interactive Plot 2D: zoom by mouse wheel
	plot2D (sin(x)) show diff and integral curves
	parametric curve in 2D
	contour plane surface in 2D
	diff2D (sin(x))
	integrate2D (sin(x))
	seimd2D (sin(x))
	ode plot graphically solve y'=sin(x)
	re2D(sqrt(x)) show 2 curves of real and imaginary in real variables
	im2D(sqrt(x)) show 2 curves of real and imaginary in imag variables
7th row	2D + 3D Plot: zoom by mouse wheel
	plot3D(sin(x))
	parametric3D(t,t,t)
	contour3D(x*y)
	implicit3D(xyz-t)
	wireframe3D(x*y) wireframe in 3D
	parametric curve in 3D
	complex3D(sqrt(x)) show complex function in complex variables
	Show function graph. sin ?
	AI chat GPT ??
8th row	Interactive Plot 3D : zoom by mouse wheel
	surface3D(x*y) surface in 3D
	function3D(sin(x)) surface in 3D
	section3D(x*y) in 4 graphs
	spin3D(sin(x)) in 4 graphs
	graph3D(x) in 10 styles
	for equation, vector, point, parametric, vector field
	data3D(x,y,z,c,t) 3D, 4D, 5D data in 10 styles
	for explicit surface, polar explicit surface, implicit surface, line, parametric curve, parametric surface, point, vector, vector field, toggle switch, variable, function, variable slider
	clear x
	All Clear memory clear(0)

First line of buttons are for algebra to return function, second line of button are for calculus to return function, third line of buttions are for discrete math with default index variable k to return value, forth line of buttions are for numeric compution to return number. 5th and 6th line of buttions are to plot2D graph. 7th and 8th lines of buttion are to plot3D graph. The same color buttons are a pair of inverse operators, its result can be checked each other if it returns origial function or not.

MathHandbook

What is mathHandbook?

the AI Math Handbook Calculator has the function of machine learning. It is unique in the world to solve the function of any order (such as complex order) differential equations. Enter mathematical formulas on the Mathematics Handbook website, click continuously to calculate calculus, solve equations, give analytical solutions and numerical solutions and diagrams, interactively zoom in the drawing, and zoom in with the mouse wheel. You can use it on your mobile phone to learn computing and development anytime, anywhere.

http://mathhand.com

It has three versions:

Phone version: run on any phone online. It does not requires to download anything.
Java version: Java Applet run on any computer that support Java online and off-line. Please contact us if you want it.
PC version: DOS version run on PC. Its old name is SymbMath, you can download it.

MathHandbook - Computer Algebra System symbolic computation.

SymbMath - PC DOS version of symbolic computation Computer Algebra System.

Rules:

put function arguments in parentheses: sin(x) -- correct, sin x -- incorrect; do not omit multiplication: x*sin(x) -- correct, x sin(x) -- incorrect. x**y or pow(x,y) for power. Usual keywords are lowercase, which are different from uppercase, e.g. sin is different from Sin. Its default variable is small letter x, but its default index variable in discrete math is k.

How to use?

see help

Example:

to do input

clear f(x) clear(f(x))

add new function f(x) = `x^2` ; f(2) f(x) = x^2; f(2)

add new rule `d/dx` f(x_) := sin(x) d(f(x_),x_) := sin(x);

add new rule of integrate `int` f(x_) dx := cos(x) integrate(f(x_),x_) := cos(x);

diff `d/dx sin(x)` d(sin(x),x)

2nd order diff `d^2/dx^2 sin(x)` d(sin(x),x,2)

0.5 order diff `d^(0.5)/dx^(0.5) sin(x)` d(sin(x),x,0.5)

minus order diff `d^(-0.5)/dx^(-0.5) sin(x)` d(sin(x),x,-0.5)

nth order diff `d^n/dx^n sin(x)` nthd(sin(x))

inverse inverse( sin(x) ) inverse(sin(x))

limit `lim_(x->oo) log(x)/x` lim(log(x)/x,x=inf)

diff `d/dx | _(x=1) sin(x)` d(sin(x), x=1)

2nd diff `d^2/dx^2 | _(x=1) sin(x)` d(sin(x), x=1,2)

integrate `int` sin(x) dx integrate(sin(x), x)

0.5 order integrate `int` sin(x) `(dx)^0.5` integrate(sin(x), x,0.5)

define integrate `int_1^2` sin(x) dx integrate(sin(x), x,1,2)

sum ∑ k sum(k)

partial sum 1+2+ .. +x = ∑ x sum(x,x,0,x)

sum 1+2+ .. +5 = ∑ x sum(x,x,0,5,1)

unlimit sum 1/0!+1/1!+1/2!+ .. +1/x! = `sum_0^oo 1/(x!)` sum(1/x!, x,0,inf)

taylor expand taylor(exp(x)) taylor(exp(x), x,5)

tangent() at x=0, tangent( sin(x) ) tangent(sin(x), x=0)

solve( 2x+3y=5, x,y ) solve( 2x+3y=5, x,y )

solve ODE dsolve( y'=sin(x+y) ) dsolve( y'=sin(x+y) )
numeric n( sin(30 degree) ) n( sin(30 degree) )

to do	input
clear f(x)	clear(f(x))
add new function f(x) = `x^2` ; f(2)	f(x) = x^2; f(2)
add new rule `d/dx` f(x_) := sin(x)	d(f(x_),x_) := sin(x);
add new rule of integrate `int` f(x_) dx := cos(x)	integrate(f(x_),x_) := cos(x);
diff `d/dx sin(x)`	d(sin(x),x)
2nd order diff `d^2/dx^2 sin(x)`	d(sin(x),x,2)
0.5 order diff `d^(0.5)/dx^(0.5) sin(x)`	d(sin(x),x,0.5)
minus order diff `d^(-0.5)/dx^(-0.5) sin(x)`	d(sin(x),x,-0.5)
nth order diff `d^n/dx^n sin(x)`	nthd(sin(x))
inverse inverse( sin(x) )	inverse(sin(x))
limit `lim_(x->oo) log(x)/x`	lim(log(x)/x,x=inf)
diff `d/dx \| _(x=1) sin(x)`	d(sin(x), x=1)
2nd diff `d^2/dx^2 \| _(x=1) sin(x)`	d(sin(x), x=1,2)
integrate `int` sin(x) dx	integrate(sin(x), x)
0.5 order integrate `int` sin(x) `(dx)^0.5`	integrate(sin(x), x,0.5)
define integrate `int_1^2` sin(x) dx	integrate(sin(x), x,1,2)
sum ∑ k	sum(k)
partial sum 1+2+ .. +x = ∑ x	sum(x,x,0,x)
sum 1+2+ .. +5 = ∑ x	sum(x,x,0,5,1)
unlimit sum 1/0!+1/1!+1/2!+ .. +1/x! = `sum_0^oo 1/(x!)`	sum(1/x!, x,0,inf)
taylor expand taylor(exp(x))	taylor(exp(x), x,5)
tangent() at x=0, tangent( sin(x) )	tangent(sin(x), x=0)
solve( 2x+3y=5, x,y )	solve( 2x+3y=5, x,y )
solve ODE dsolve( y'=sin(x+y) )	dsolve( y'=sin(x+y) )
numeric n( sin(30 degree) )	n( sin(30 degree) )

algebra: convert.

calculus: limit, nth derivative, differentiation, integral, fractional calculus, convert to integral.

equation: Inequalities, congruence equation, Dorphine equation, modulus equation, recurrence equation, (fractional) differential equation, (fractional) integral equation, by solve(), dsolve(), lasolve(), rsolve().

discrete math: sum, partial sum, indefinite sum, infinite sum, convert to sum.

interactive plot zoom by mouse wheel: polar plot, parametric plot, implicit plot, tangent plot, secant plot, plot, plot2D, plot3D, parametric3D, parametric3Dxy, implicit3D, complex3D, spin3D

animation:

Please read its example and manual of symbolic computation Computer Algebra System.