For example, in the case of our previous spline function, newcubic, we have We can also determine the differentiability class of a piecewise continuous function. It turns out to be a well-behaved, non-piecewise function. For example,Ĭonvert ⁡ 1 − x, ' piecewise 'Ĭonvert ⁡ − signum ⁡ x ⁢ 1 − x, ' piecewise ' Other piecewise functions can also be converted to piecewise and be properly manipulated. Newcubic ≔ CurveFitting Spline 0, 1, 2, 3, 0, 1, 4, 3, x Normal ⁡ convert ⁡ heavyf, ' piecewise ' Heavyf := x ⁢ Heaviside ⁡ 1 + x − x − x 2 ⁢ Heaviside ⁡ x − 1 + x 2 ⁢ Heaviside ⁡ 1 + x + sin ⁡ x − 1 ⁢ Heaviside ⁡ x − 1 x − 1ĭistributions can be converted back to piecewise functions. Note: This works because discont is able to determine the potential discontinuities of piecewise functions. Where Si(x) is the Sine integral function. Using the same function, f ( x ), find its piecewise derivative.įprime ≔ &DifferentialD &DifferentialD x f Examples of solving DEs will be illustrated later. Such functions can be plotted to determine their behavior.īesides evaluating limits, you can do operations such as computing derivatives, integrating, and solving differential equations with piecewise functions. The next several Maple command lines make use of the following piecewise function:į := piecewise ⁡ x ≤ − 1, − x, x ≤ 1, x 2, 1 īecause of the division by zero, points such as x = 1 cannot be substituted. Every piece is specified by a Boolean condition followed by an expression.

The piecewise function has a straightforward syntax. This worksheet contains a number of examples of the use of the piecewise function.

Piecewise graph