Fractional Calculus Computer Algebra System math software

Clicking function enters it into Calculator, and moving mouse over it shows its text.
+ - * / ^ ! ^o `oo` `alpha` `beta` `gamma` `theta` `pi` ( )
sin(x) cos(x) tan(x) cot(x) sec(x) csc(x)
`sin^(-1)(x)` `cos^(-1)(x)` `tan^(-1)(x)` `cot^(-1)(x)` `sec^(-1)(x)` `csc^(-1)(x)`
sinh(x) cosh(x) tanh(x) coth(x) sech(x) csch(x)
`sinh^(-1)(x)` `cosh^(-1)(x)` `tanh^(-1)(x)` `coth^(-1)(x)` `sech^(-1)(x)` `csch^(-1)(x)`
`x^2` `sqrt(x)` `root3(x)` `e^-x` exp(x) log(x) `log_10`(x) |x| sgn(x) `C_x^2` `H_x^2`
`Gamma(x)` `gamma(2,x)` `psi(x)` erf(x) `Phi(x)` Ei(x) li(x) si(x) ci(x) `zeta(x)` `E _0.5 (x)`
f(x) `f^-1(x)` `int`f(x) dx `int_0^1`f(x) dx `d/dx`y(x) `(d^(1/2) y)/dx^(1/2)` `y^((1))(x)` y'

zoom graph by mouse wheel

How to use? There are many ways:

Input or click sin(x) , click for integration, click button for derivative to check its result, click again for second derivative, click to inverse function, click for definition, click to simplify, click ......
Input the unkown y as seond argument,
sin(x)=cos(y), y
then click the button to solve for unknown y.
Input command by use of the first function as command, e.g.
- integrate sin(x) as x from 0 to 1
then hit the button or the ENTER key in your keybord.
Input function, e.g.
- int(sin(x))
Input function by use of "," or ";" as separator for multistatements, e.g.
- int(sin(x)), d(sin(x))
Input question mark ? to show a list of function, i.e.
- ?
Input function and question mark ? to show its function source. e.g.
- sin(x)

To do	Button
algebra	1st row
simplify `sin^((0.5))(x)`
expand `(x-1)^2`
factor `(x^2-1)`
convert sin(x) to exp(x)
convert asin(x) to log(x)
convert exp(x) to sin(x)
convert sin(x) to sinh(x)
solve equation for x, solve( exp(x)+exp(-x)=4 )
Show function source. sin(x)?
calculus: default variable is x	2nd row
convert sin(x) to integral
tangent sin(x)
differentiate `d/dx sin(x)`
integrate ∫ sin(x) dx
infinite integration integrate( exp(-x) as x->oo )
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)`
laplace transform
dsolve solve (fractional) differential equation for y, dsolve( y'=(x-y)! ), dsolve `d^0.5/dx^0.5 y=sin^((-0.5))(x)`
discrete math: default index variable is k	3th row
convert sin(x) to sum
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`
rsolve solve functional equation f(x+1)-f(x)=x
Numeric math	4th row
definition ( sinh(x) )
inverse ( sin(x) )
limit lim( sin(x)/x as x->0 )
limoo lim( 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 )`
numeric answer
Interactive Plot: zoom by mouse wheel	5th row
Clear input
polar plot polarplot(sin(4*x))
parametric plot parametricplot( x=sin(t) and y=cos(2*t) )
implicit plot `x^2+y^2=1 and x^2+y^2=4`
tangent plot tangentplot(sin(x))
overlap plot sin(x)
plot sin(x) and `x^2`
plot3d plot3d(sin(x))
symbolic answer

The same color buttons are a pair of inverse operators, its result can be checked each other if it returns origial function or not. 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.

Math Handbook Calculator

- Computer Algebra System of Fractional Calculus

Example:

MathHandbook