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Math Handbook 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)` `((3),(x))`
x! 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)` `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'

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
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)
convert 2-i to complex() comvert 2-i to complex(2,-1)
inverse( sin(x) )
calculus: default variable is x 2nd row
convert sin(x) to integral definition
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)`
dsolve solve (fractional) differential equation for y,
dsolve( y'-y-x^x=0),
test solution for equation and diff equation
discrete math: default index variable is k 3th row
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`
rsolve solve functional equation f(x+1)-f(x)=x
Numeric math 4th row
definition( sinh(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 )`
solve equation for x, solve( exp(x)+exp(-x)=4 )
numeric answer
Interactive Plot: zoom by mouse wheel 5th row
plot sin(x) and `x^2`
implicit plot `x^2+y^2=1 and x^2+y^2=4`
parametric plot parametricplot( x=sin(t) and y=cos(2*t) )
tangent plot tangentplot(sin(x))
secant plot secantplot(sin(x))
polar plot polarplot(sin(4*x))
ode plot graphically solve y'=sin(x)
overlap plot sin(x)
Interactive Plot 2D: zoom by mouse wheel 6th row
plot2D (sin(x)) show diff and integral curves
taylor2D (sin(x))
diff2D (sin(x))
integrate2D (sin(x))
to inte (sin(x))
integral2D (sin(x))
complex2D(sqrt(x)) show real and imaginary curves in real domain
Interactive Plot 3D: zoom by mouse wheel 7th row
complex3D(sqrt(x)) show complex function in complex domain
Interactive Plot 3D with 3 parameters 8th row
plot3DIE in IE plot3DIE(sin(x))
Show function graph. Input cos(x) , click the ? button

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.


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.


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


    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.
    2. Java version: Java Applet run on any computer that support Java online and off-line. Please contact us if you want it.

    3. PC version: DOS version run on PC. Its old name is SymbMath, you can download it.
    MathHandbook - Computer Algebra System symbolic computation.
    1. Brief
    2. manual
    3. mathHandbook.doc
    4. Developer document
    5. Functions
    6. Examples

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

    1. table of content
    2. brief
    3. manual
    4. SymbMath.doc
    5. Lists of Review
    6. Review
    7. download


    post to QQ group 614057790 or forum.