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 `x^2` `sqrt(x)` `root3(x)` `e^-x` exp(x) log(x) `log_10`(x) |x| sgn(x) `C_x^2` `H_x^2`
x! `Gamma(x)` `gamma(2,x)` `psi(x)` erf(x) erfi(x) `Phi(x)` Ei(x) li(x) si(x) ci(x) `zeta(x)` `E _0.5 (x^0.5)`
f(x) = x; `sum _x f(x)` `int`y(x) dx `int` y(x) `(dx)^0.5` `int_0^1`y(x) dx `d/dx`y(x) `(d^(1) y)/dx^(1)` `y^((1))(x)` y'

programing

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
Clear input
symbolic answer
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)`
lasolve solve diff equation by 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
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`
Interactive Plot 3D: zoom by mouse wheel	6th row
plot3D plot3DIE(sin(x))
plot3D plot3D(sin(x))
plot3D contour3D(x*y)
plot3D wireframe3D(x*y)
plot3D implicit3D(xyz)
plot3D complex3D(x)
Interactive Plot 3D by 3 parameters: zoom by mouse wheel	7th row
plot3D parametric3D(t,t,t)
plot3D parametric3Dxy(x,y,x*y)
plot3D wireframe3Dxy(x,y,x*y)
help ? gamma?

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.

Example:

Add new function f(x) = `x^2`; call f(2)
f(x) = x^2; f(2)

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

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

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: polar plot, parametric plot, implicit plot, tangent plot, secant plot, plot, plot3d. zoom by mouse wheel.

animation:

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

MathHandbook

What is mathHandbook?

It is an online graphic calculator and computer algebra system with learning. It can perform exact, numeric, symbolic and graphic computation, e.g. any order of derivative, fractional calculus, fractional differential equation, symbolic differentation and integration, indefinite sum, interactive plot. It is a programming language, e.g. add new fractional derivatives and integrals, conditional or recursive functions, procedures, and rules.
It can run on any mobile with Internet, and any computer with Java.
It is Computer Algebra System for symbolic computation of any order of fractional derivative. 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.

QQ group 614057790

See Also

Math Handbook Calculator

- Computer Algebra System of Fractional Calculus

Example:

MathHandbook