Wolfram|Alpha Examples Back By now you might have heard about Wolfram|Alpha. It is an online computational engine which is a work in progress. It is useful for our classes for doing some quick data lookup, computations, plots, etc. You should explore the many examples and widgets that are at their site.  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 Using Piecewise function 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 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 What is Wolfram Alpha? Ask Wolfram - Part 1, Part 2 Learn by Examples ... see physics section Widgets - for Quick Wolfram|Alpha routines Eigenvalue Problems - 2x2, 3x3 Other Stuff Dynamical systems Logistic Map or Plot[{2.5*((1- x) x), x}, {x, 0, 1}] Top E-Mail: Dr. Russell Herman Last Updated: January 11, 2018

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