Simpson's rule approximates the integrand by a piecewise quadratic function. Integration of the beam equation again results in piecewise polynomial deflection. In this case, a spline is a piecewise polynomial function. In mathematics, a spline is a special function defined piecewise by polynomials. The problem can be avoided by using spline curves which are piecewise polynomials. The real absolute value function is a piecewise linear, convex function. The square of each of these is approximated using piecewise linear circuits. Here C refers to any of the categories of smooth, piecewise linear, or topological manifolds. It is a periodic, piecewise linear, continuous real function. Among other things, he showed that every piecewise continuous function is integrable. This contrasts strongly with higher-dimensional manifolds which need not admit smooth or piecewise linear structures. The notion of a piecewise linear function makes sense in several different contexts. More robust methods have been explored, such as branch and bound and piecewise linear network. The lemma is implicit in the use of piecewise functions. The degree-0 functions formula 9 are piecewise constant functions.