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**Contents:**

Title and Synopsis

Basics

Try It!

Elementary School

Middle and High School

Calculus

Combinatorics

Linear Algebra

Differential Equations

Other Advanced Topics

It's Not (Only) About Math!

More Examples (and Data!)

Less Is More

So Is It Perfect Yet?

What About Google?

Possible Implications

A Threat?

Resources

[Note: This article appears best using the Firefox browser.]

Consider the query "d^2 y/dx^2 + 4dy/dx + 5y = 0." Wolfram|Alpha interprets this as a second-order linear differential equation and provides the general solution and plots of individual solutions. If you prefer an initial value problem, try "y''+y=0, y(0)=2, y'(0)=1."

If you want a nonhomogeneous example, try "y''(t) + y(t) = sin t." Here's a nonlinear example: "f'(t) = f(t)^2 + 1." And here's an example involving a parameter: "y'(t)=a t y(t)." Wolfram|Alpha knows the Bessel functions--try "(-4+x^2) w(x)+x w'(x)+x^2 w''(x) = 0." (But following the links for further information about Bessel's equation or either of the two types of Bessel functions involved will take you out of this article.)

up[*Note:* Contents of frame come from
wolframalpha.com and are not maintained
by *Loci*]