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Math Handbook Calculator

- Computer Algebra System of Fractional Calculus

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)
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
differentiate `d/dx sin(x)`
integrate ∫ sin(x) dx
infinite integration `int_0^oo ( exp(-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)`
ODE solve ordinary differential equation for y,
ODE( y'-y-x^x=0),
PDE solve partial differential equation for y,
PDE( ds(y,t)-ds(y,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
length length(sin(x))
area area(sin(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))
integral (sin(x))
polar plot polarplot(sin(4*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))
seimd2D (sin(x))
complex2D(sqrt(x)) show real and imaginary curves in real domain
ode plot graphically solve y'=sin(x)
Interactive Plot 3D: zoom by mouse wheel 7th row
plot3D(sin(x))
implicit3D(x*y*z-t)
contour3D(x*y)
wireframe3D(x*y)
spin3D(sin(x))
complex3D(sqrt(x)) show complex function in complex domain
Interactive Plot 3D with 3 parameters 8th row
plot3DIE in IE plot3DIE(sin(x))
parametric3D(t,t,t)
parametric3Dxy(x,y,x*y)
wireframe3Dxy(x,y,x*y)
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.

Rules:

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.

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?

    the Math Handbook Calculator has the function of machine learning. It is unique in the world to solve the function of any order (such as 0.5 order) differential equations. Enter mathematical formulas on the Mathematics Handbook website, click continuously to calculate calculus, solve equations, give analytical solutions and numerical solutions and diagrams, interactively zoom in the drawing, and zoom in with the mouse wheel. You can use it on your mobile phone to learn computing and development anytime, anywhere.

    http://mathhand.com

    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

    Question?

  • bugs post to QQ group 614057790 or forum.
  • 
    Home | list | wiki | about | donate | index | forum | help | 中文 | translated from Chinese

    Function

    Ai
    airyAi
    airyBi
    abs
    acos
    acosh
    acot
    acoth
    acsc
    acsch
    angle
    area
    arg
    argument
    asec
    asech
    asin
    asinh
    assume
    atan
    atan2
    atanh
    arccos
    arccosh
    arccot
    arccoth
    arccsc
    arccsch
    arcsec
    arcsech
    arcsin
    arcsinh
    arctan
    arctanh

    Bi
    beta
    smallbeta
    bell
    bernoulli
    binomial
    block

    C
    catalan
    cbrt
    ceil
    ci
    circle
    cis
    Cl
    Clausen
    chi
    combination
    combine
    complete d
    complex
    complex2D
    complex3D
    conjugate
    convert
    cos
    cosh
    csc
    csch
    csgn

    d
    Dawson
    def
    define
    definition
    deg
    degree
    delta
    diff
    difference
    digamma
    dilog
    doublefactorial
    ds
    dsolve

    E
    Ei
    Ein
    En
    evaluate
    eta
    erf
    erfc
    erfi
    euler
    exp
    expand
    expandexp
    expandtrig

    factor
    factorial
    factorial2
    factorialpower
    fallingfactorial
    fib
    fibonacci
    floor
    For
    for
    fourier
    fresnelC
    fresnelS

    Gamma
    gamma
    smallgamma
    GammaQ
    gammaP
    gauss
    gaussi
    gaussian
    gcd
    gsolution

    H
    harmonic
    has
    hasnot
    hypot

    If
    if
    im
    infint
    infints
    infsum
    infsums
    int
    integral
    integrate
    integrates
    inverse
    inverseerf
    inverseerfc
    inversefactorial
    inverseGamma
    inverselaplace

    isatom
    isconstant
    iscomplex
    isfloat
    iseven
    isfree
    isfunction
    isinteger
    isnumber
    isodd
    isprime

    L
    lamberW
    lucas
    laplace
    lasolve
    last
    left
    length
    Lerch
    lg
    li
    list
    lim
    limit
    limoo
    ln
    log
    log10
    logBeta
    logGamma
    loggamma

    max
    min
    mittag
    mod
    modInverse


    n
    name
    nextprime
    nint
    nlim
    not
    nsolve
    nsum
    nthd

    ODE
    ode
    oval

    P
    Phi
    parametricplot
    partialsum
    pde
    PDE
    pdsolve
    plot
    plot2D
    plot3D
    plot3DIE
    pochhammer
    polar
    polard
    polarplot
    poly
    polyroot
    polygamma
    polylog
    point
    pow
    power
    powermod
    prime
    prod
    product
    psi
    psolve
    psolution
    psum

    random
    range
    re
    recurrence
    remainder
    replace
    right
    risingfactorial
    rsolve
    round
    root

    S
    sec
    sech
    secantplot
    semicircle
    semid
    semiint
    series
    sgn
    sign
    si
    simplify
    sin
    sinc
    sinh
    size
    smallgamma
    solve
    sort
    Sophomore
    Sophomore1
    sqrt
    Stirling1
    Stirling2
    sum
    sum0inf
    sum0n
    sum1inf
    sum1n
    swap

    tan
    tani
    tanh
    tangent
    tangent plot
    taylor
    test
    theta
    timer

    tocomplex
    tocos
    tocosh
    todegree
    toerf
    toexp
    togamma
    tofactorial
    tolog
    toint
    tointegral
    tomittag
    tosum
    toparfrac
    topolar
    topolard
    topoly
    topolyroot
    topow
    topower
    tosin
    tosinh
    toradian
    totrig
    totrigh

    trigamma
    type

    value
    vector

    W
    While
    when

    x(1,t)
    y(1,x)
    zeta