15.2.1  Boxcar function: boxcar

The boxcar command creates a function which is 0 everywhere except in a given interval, where it is 1.

• boxcar takes three arguments:
  • a,b, two real numbers.
  • x, an identifier or expression.
• boxcar(a,b,x) returns θ(x−a)−θ(x−b), where θ is the Heaviside function (see Section 6.8.9). The resulting expression defines a function which is zero everywhere except within the segment [a,b], where its value is equal to 1.

Examples.

• Input:
  boxcar(1,2,x)
  Output:

  θ

  ⎛ ⎝

  x−1

  ⎞ ⎠

  −θ

  ⎛ ⎝

  x−2

  ⎞ ⎠

• Input:
  boxcar(1,2,3/2)
  Output:

  1

• Input:
  boxcar(1,2,0)
  Output:

  0