In the chapter, the space Sm(Δ,m − 1) of piecewise polynomial splines of degree m and differentiable up to the order m − 1 is introduced. In particular, the space S1(Δ, 0) of piecewise linear splines and the space S3(Δ, 2) of cubic splines are determined . Theorems on interpolation by the splines are stated and proved. The space S11(Δ, 0, 0) of belinear splines and the space S33(Δ, 2, 2) of be-cubic splines in two variables defined on rectangular grids are presented. On triangular grids the spaces Π1 (Δ) and Π3 (Δ) are considered. Mathematica modules have been designed for solving problems associated with application of splines. The chapter ends with a set of questions.
Keywords: Polynomial splines, linear splines, cubic splines.