﻿ ﻿﻿ Fractional Calculus Computer Algebra System math software + + =  # MathHandbook Calculator

## - Computer Algebra System of Fractional Calculus

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) root2(x) e^-x exp(x) log(x) log_10(x) |x| re(x) im(x) W(x) C_x^2
x! Gamma(x) gamma(2,0,x) psi(x) erf(x) erfi(x) Ai(x) Ei(x) li(x) si(x) S(x) zeta(x) E _0.5 (x^0.5)
f(x) = x; sum _x f(x) inty(x) dx int y(x) (dx)^0.5 int_0^1y(x) dx d/dxy(x) (d^(1) y)/dx^(1) y^((1))(x) y'
programing

zoom graph by mouse wheel

How to use? There are many ways:

1. 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 ......
2. Input the unkown y as seond argument,
sin(x)=cos(y), y
then click the button to solve for unknown y.
3. Input command by use of the first function as command, e.g.
then hit the button or the ENTER key in your keybord.
4. Input function, e.g.
5. Input function by use of "," or ";" as separator for multistatements, e.g.
6. Input question mark ? to show index, i.e.
7. Input function and question mark ? to show its function source. e.g.
8. Input function and then click the question mark ? button to show its function graph. e.g.
 To do Button Clear input symbolic answer numeric 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) complex(sqrt(x)) show real and imaginary curves solve equation for x, solve( exp(x)+exp(-x)=4 ) 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 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 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 ) Interactive Plot: zoom by mouse wheel 5th row plot sin(x) and x^2 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) plot2D sin(x), solve diff eq graphically Interactive Plot 3D: zoom by mouse wheel 6th row plot3DIE in IE plot3DIE(sin(x)) plot3D plot3D(sin(x)) plot3D contour3D(x*y) plot3D wireframe3D(x*y) plot3D implicit3D(x*y*z) plot3D spin3D(sin(x)) Interactive Plot 3D with 3 parameters 7th row plot3D parametric3D(t,t,t) plot3D parametric3Dxy(x,y,x*y) plot3D wireframe3Dxy(x,y,x*y) plot3D complex3D(x) Show function graph. Input cos(x) , click the ? button

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 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.

## 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:

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