Experimental data are often in need of smoothing without a pre-determined trend line equation. This manuscript demonstrates how spreadsheet software can be programmed to smooth experimental data via cubic splines. Once the trend lines (splines) have been constructed, it is also simple to interpolate values and calculate derivatives and integrals. The formulas to carry out the calculation are li...

Fair webs are energy-minimizing curve networks. Obtained via an extension of cubic splines or splines in tension to networks of curves, they are efficiently computable and possess a variety of interesting applications. We present properties of fair webs and their discrete counterparts, i.e., fair polygon networks. Applications of fair curve and polygon networks include fair surface design and a...

A boundary value problem for a 4-th order self-adjoint ordinary differential equation is considered in the case where the coefficients of the equation and its right-hand side can be nonsmooth (discontinuous, concentrated or rapidly oscillating functions). Generalized cubic splines of deficiency 1 depending on the major coefficient of the equation are applied. An error analysis of finite element...