﻿ ﻿﻿ AI math handbook calculator - Fractional Calculus Computer Algebra System software
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# AI Math Handbook Calculator

## - Computer Algebra System of Fractional Calculus

coding zoom graph by mouse wheel

Button To do
Clear input
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 Δk^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
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)
Show function graph. sin ?
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)
complex2D(sqrt(x)) show 2 curves of real and imaginary in real variables
AI chat GPT ??
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
parametric surface in 3D parametrics3D(u,v)
complex3D(sqrt(x)) show complex function in complex variables
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:

1. Phone version: run on any phone online. It does not requires to download anything.

3. 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.

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) )

• 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.

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abs
acos
acosh
acot
acoth
acsc
acsch
Ai
airyAi
airyBi
angle
area
arg
argument
asec
asech
asin
asinh
assume
atan
atan2
atanh
arccos
arccosh
arccot
arccoth
arccsc
arccsch
arcsec
arcsech
arcsin
arcsinh
arctan
arctanh