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Symbolic Calculator

- Computer Algebra System for Symbolic Computation of Fractional Calculus

`int_0^oo ` Math Handbook dx = MathHandbook.com






How to use? There are three ways:

  1. Input or click sin(x) , then click the button for derivative, click again for second derivative, click to solve differential equation, click to differentiate solution for double check, click for integration, click to inverse a function, click for definition, click to simplify, click ......
  2. Input command, e.g.
    then hit the button or the ENTER key in your keybord.
  3. Input function by use of comma "," as separator for multi functions, e.g. then hit the button or the ENTER key in your keybord.
To do
Button
algebra 1st row
expand`(x-1)^2`
factor`(x^2-1)`
convert sin(x) to exp(x)
convert exp(x) to sin(x)
convert sin(x) to sinh(x)
convert sin(x) to integral
definition( sin(x) )
calculus 2nd row
limit `lim _(x->oo) log(x)/x`
differentiate `d/dx sin(x)`
integrate ∫ sin(x) dx
infinite integration `int_0^oo e^-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)`
dsolve solve (fractional) differential equation,
dsolve( y'=(x-y)! ) dsolve `d^0.5/dx^0.5 y=sin^((-0.5))(x)`
evaluate inert function `sin^((0.5))(x)`
discrete math 3th row
convert sin(x) to sum
difference Δ`x^2`
Indefinite sum ∑ x
partial sum `sum_(k=0)^n` k
partial sum `sum_(k=1)^n` k
infinite sum `sum_(k=0)^oo x^k/(k!)`
infinite sum `sum_(k=1)^oo x^k/(k!)`
series( sin(x) )
rsolve solve recurrence equation y(x)-y(x-1)=x
simplify
Numeric math 4th row
numeric limit `lim _(x->0) sin(x)/x`
numeric integrate `int _1^2` sin(x) dx
numeric sum `sum _(x=1)^8` x
numeric solve equation nsolve`( x^2-1=0 )`
Taylor series expansion taylor(sin(x))
inverse( sin(x) )
solve equation solve( sin(x)=cos(x) )
numeric answer
Interactive Plot: mouse wheel to zoom 5th row
Clear input
All Clear input and memory and plot
polar plot r=sin(4*x)
parametric plot x=sin(t) and y=cos(2*t)
implicit plot `x^2-y^2=2 and x-y=1`
plot sin(x) and `x^2`
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, and its default value is 0.

Examples:

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

  • f(x) = x^2

    Add new rule of derivative `d/dx` f(x_) := 2*x

  • d(f(x_),x_) := 2*x

    Add new rule of integral `int` f(x) dx := F(x)

  • integrate(f(x_),x_) := F(x)

    algebra:
    convert sin(x) to exp(x),

  • convert sin(x) to exp
  • toexp( sin(x) )

    inverse

  • inverse( sin(x) )
    plot multi values of inverse function
  • inverse( y=sin(x) )

    tangent at x=1

  • tangent( sin(x),x=1 )
    by default x=0
  • tangent( sin(x) )

    solve inequalities,

  • solve( 2*x-1>0 )
  • solve(2*x-1>0)

    solve equation,

  • solve( x^2-5*x+6=0 )
    by default equation = 0
  • solve( x^2-5*x+6 )

    polymonial:
    topoly convert roots to poly(a and b) as holder of polymonial roots,

  • convert (2 and 3) to poly()
  • topoly( 2 and 3 )
    activate poly() to polymonial
  • activate( poly(2 and 3) )

    topoly convert polymonial to poly(a,b,c) as holder of polymonial coefficients,

  • convert `x^2-5*x+6` to poly
  • topoly( `x^2-5*x+6` )
    activate poly() to polymonial
  • activate( poly(6,-5,1) )

    calculus:
    limit

  • `lim_(x->oo) log(x)/x`
    by default x=infinity,
  • lim(log(x)/x)

    Differentiate

  • `d/dx sin(x)`
  • d(sin(x))

    Second order derivative

  • `d^2/dx^2 sin(x)`
  • d(sin(x),x,2)

    sin(0.5,x) is inert holder of the 0.5 order derivative `sin^((0.5))(x)`, it can be activated by activate():

  • activate( sin(0.5,x) )
  • `d^(0.5)/dx^(0.5) sin(x)`
  • d(sin(x),x,0.5)

    semiderivative

  • `d^(0.5)/dx^(0.5) sin(x)`
  • semid(sin(x))

    Derivative at x=1

  • `d/dx | _(x=1) x^6`
  • d(x^6, x=1)

    Second order derivative at x=1

  • `d^2/dx^2 | _(x=1) x^6`
  • d(x^6, x=1,2)

    integrate

  • `int` sin(x) dx
  • integrate(sin(x))

    semiintegrate

  • `d^(-0.5)/dx^(-0.5) sin(x)`
  • semiint(sin(x))

    Definite integration

  • `int_1^2` sin(x) dx
  • integrate(sin(x), x, 1,2)
  • integrate sin(x) as x from 0 to 1

    differential eqaution:
    dsolve differential equation,

  • dsolve( y' = sin(x-y) )
  • dsolve( dy/dx=cos(x-y) )
  • dsolve( ds(y)=tan(x-y) )

    dsolve fractional differential equation,

  • dsolve( `(d^0.5y)/dx^0.5=sin^((-0.5))(x)` )
    odetest test solution for differential equation,
  • odetest( exp(2x), `dy/dx=2y` )
  • odetest( exp(4x), `(d^0.5y)/dx^0.5=2y` )

    discrete math:
    Indefinite sum

  • ∑ x
  • sum(x)

    partial sum of 1+2+ .. +x = ∑ x

  • partialsum(x)

    Definite sum of 1+2+ .. +5 = ∑ x

  • sum(x,x,0,5,1)

    Infinite sum of 1/0!+x/1!+ .. +x^k/k! = `sum_0^oo x^k/(k!)`

  • infsum(x^k/k!,k)

    Taylor series expansion at x=0,

  • taylor( exp(x) as x=0 )
    by default x=0,
  • taylor(exp(x))

    series expand not only to taylor series,

  • series( exp(x) )
    but aslo to other series expansion,
  • series( zeta(2,x) )

    numeric math:
    numeric solve equation,

  • nsolve( x^2-5*x+6=0 )
  • nsolve(x^2-5*x+6)

    numeric integrate, by default x from 0 to 1.

  • nint( x^2-5*x+6,x,0,1 )
  • nint x^2-5*x+6 as x from 0 to 1
  • nint sin(x)

    numeric computation,

  • n( sin(30 degree) )
  • n sin(30 degree)


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

    MathHandbook

    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 phone and tablet 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
    


    See Also

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