We've previously found that Heaviside functions are useful for simulating a number of piecewise functions.

			The Delta function, which can be constructed from two Heaviside functions, is extremely useful for modeling an impulse, such as striking a mass-spring system with a hammer.

			The Delta function, δ(t), is defined to be zero everywhere except at the place its argument (t) is zero.  At that point it is infinitely high, but in such a way that its area is unity.  It is best thought of as the limit (as w -> 0) of a rectangle whose width is w and whose height is 1/w.

			One of the most useful properties of the Delta function is its "sifting" property, that is, the integral from -∞ to +∞ of the product of a Delta function and another function is equal to the value of the other function at the point the Delta function is nonzero:

			Example:

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