• This page employs the very nice Algebrite CAS for JS for all symbolic manipulations.
• Mathematical output is typset using MathJax. If you do not get pretty output, reload. Sometimes the script is not served.
• My only contributions are the interface and graphing commands.

Examples

Type code in the smaller input box at the top of the page and press enter. Output should appear in the large box along with a copy of the input you type. If you click on the copy of your input in the output box, it will be copied back to the input box.

Clicking on the code examples below will copy them to the input box.

• Functions
  • Define a new function of one variable.

    f(x)=x^2+sin(x)

  • Evaluate a function.

    f(2)

  • Evaluate a function and force an approximate result.

    f(2.0)

  • Evaluate a function using a built in constant.

    f(pi)

  • Define a function of two variables.

    f(x,y)=sin(x^2+y^2)

• Graphing functions
  • Graph a function of one variable. That variable is assumed to be x

    plot(x*(x-1)*(x+1))

  • You can modify plotting parameters using the gui once you have graphed a functions. However, you can also modify them with the command below. The parameters that can be modified this way are MINX, MAXX, MINY, MAXY, MINZ, MAXZ and, for parametric plots, MINT, MAXT, MINU, MAXU, MINV, MAXV.

    parameters(MINX=-1, MAXX=1, MINY=-0.5, MAXY=1.5)

  • Graph multiple functions at once.

    plot(sin(x), cos(x), tan(x))

  • Graph a function of two variables.

    plot3d(x*sin(y))

  • Graph a function of two variables with a custom window. The viewing window for 3d plots is forced to be symmetric, so we only set the maximum values of the variables. (This example requires you to enter two lines separately.)

    parameters(MAXX=2, MAXY=2, MAXZ=2)

    plot3d(10*x*y*exp(-(x^2+y^2)))

• Parametric Equations and Polar Coordinates
  • Graph a parametric curve in two dimensions. Variable is assumed to be t. (This example requires you to enter two lines separately.)

    parameters(MINT=0, MAXT=20)

    parametricplot(t/5*cos(t), t/5*sin(t))

  • Graph a parametric curve in three dimensions. Variable is assumed to be t. (This example requires you to enter two lines separately.)

    parameters(MINT=-5, MAXT=5)

    parametricplot3d(3*cos(t), 3*sin(t), t)

  • Graph a parametric surface. Variables are assumed to be u and v. (This example requires you to enter two lines separately.)

    parameters(MINU=0, MAXU=6.28, MINV=0, MAXV=6.28)

    parametricsurface(2.5*(1+cos(v)) cos(u), 2.5*(1+cos(v)) sin(u), 2.5*sin(v))

  • Graph a polar curve. The variable is assumed to be t

    parameters(MINT=0, MAXT=6.28,MINX=-2.1, MAXX=2.1, MINY=-2.1, MAXY=2.1)

    polarplot(1+cos(t))

• Derivatives
  • Find a derivative.

    d(x*sin(x), x)

  • Graph a function and its derivative. (This example requires you to enter two lines separately.)

    f(x)=x*(x-1)*(x+1)

    plot(f(x), d(f(x), x))

  • Find a derivative with respect to a different variable.

    d((t-1)/(t+1), t)

  • Find a second derivative.

    d(x^3+x^2+x+1, x, x)

  • Find a partial derivative.

    d(x^2*y+x*y^2, x)

  • Find a mixed partial derivative.

    d(x^2*y+x*y^2, x, y)

  • Find a gradient

    d(x^2+x*y+y^2,[x,y])

• Vector fields
  • Graph a vector field. Variables are assumed to be x and y

    vectorfield(x*y^2, x^2*y)

  • Graph a gradient. (This example requires you to enter two lines separately.)

    G=d(x*sin(y),[x,y])

    vectorfield(G[1], G[2])

• Integrals
  • Evaluate an antiderivative. Note that you can specify the variable.

    integral(x*ln(x), x)

  • Evaluate a definite integral.

    defint(1/sqrt(1-t^2), t, 0, 1)

  • Evaluate an indefinite multiple integral.

    integral(x^2*y+x*y^2, x, y)

  • Evaluate a definite multiple integral. Note that limits on the inside variable can be functions.

  • defint(3-x-y, y, 0, x, x, 0, 1)