Wolfram|Alpha Examples

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Listed here are some simple examples. Click on the link and the input and output will be displayed. If the + signs do not transfer, then copy and paste the equation.

• Simple Commands
  • expand (x+y)^5 and simplify x^2+2x*y+y^2
  • Solve equation in one variable: solve x^2+2x-5=1
  • Solve equations in 2 variables: solve {y+2x=1,x+y=2}
  • Limits: limit Sin[x]/x x->0
  • Derivatives: derivative (x*Exp[x])/Sin[x]
  • Integrals: integral Log[x] or integral Log[x], x=1,2
  • Evaluate a function 1/2*(ln(1+x)-ln(1-x))-tan(x) at x=0.0015
  • Or, Substitute x=2.5*10^(-13),1-1/sqrt(1-x) vs 1-1/sqrt(1-x) at x=2.5*10^(-13)
  • Compute series 1/2*(ln(1+x)-ln(1-x))-tan(x)
• Plots
  • plot x2, plot y=x^2, x=0,3, plot e^x from x=0 to 10
  • Multiple functions: plot sin x, cos x
  • Piecewise defined function:
    • Using Heaviside step function
      • H(x)-H(x-3)
      • plot cos(5x)*(H(x)-H(x-3)) x=0 to 5
    • Using Piecewise function
      • plot Piecewise[{{2,-2<x <2}, {x,2<= x < 3}}] x=-5 to 5
  • Implicit 2D Plot: plot x^2+xy+y^2=1
  • Parametric Plot:
    parametric plot{2 cos t, 3 sin t} or parametric plot{2 cos t, 3 sin t} t=0,pi
  • Polar Plot (Ellipse) polar plot r=2/(1+0.5 cos theta), theta=0,2 pi
  • Surface Plot: plot x^2+xy+y^2-1
• Differential equations
  • solve 3y'+5y=2 e^x
  • solve y''+3y'+5y=2 e^t
  • Damped harmonic motion: solve y''+.1y'+2y=0
  • System: solve {x' = 2 y - x, y'=x+y}

• Fourier series

  • plot sum_(k=1)^10(4/pi sin((2 k-1)*x)/(2 k-1))

  • plot sum_(k=1)^10(4/pi sin((2 k-1)*x)/(2 k-1)) x=0 to 2 pi

  • plot sum_(n=1)^10(cos(2 n pi x)/(n pi)^2- sin(2 n pi x)/(n pi)) x=0 to 4

  • plot sum_(k=1)^10(2/pi^2 cos(2(2 k-1)*pi*x)/(2 k-1)^2)

• Maple Version: plot(1/4+sum((cos(n*Pi)-1)/(n*Pi)^2*cos(2*n*Pi*x),n=1..100),x=-1..2);

• Laplace Transforms

  • laplace transform t^2 + 1

  • inverse laplace transform s/(s^2+s+1)

• What is Wolfram Alpha?

  • Ask Wolfram - Part 1, Part 2

  • Info for Calculus Students

  • Learn by Examples ... see physics section

• Widgets - for Quick Wolfram|Alpha routines

  • Parametric Plots

  • Surface Plot

  • Vector Algebra

  • Eigenvalue Problems - 2x2, 3x3

  • Divergence and Curl (Rot)

  • Laplace Transform, Inverse Laplace Transform

• Other Stuff

  • Wilmington

  • hurricane irene

  • what is the meaning of life?

  • volvo 2005

  • us population

• Dynamical systems

  • Logistic Map or Plot[{2.5*((1- x) x), x}, {x, 0, 1}]

  • http://m.wolframalpha.com/examples/Fractals.html

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