ABSTRACT
This chapter presents a new set of piecewise constant orthogonal functions called delayed unit step function (DUSF). The set of DUSF has been compared with the block pulse function (BPF) set both qualitatively and quantitatively to establish that the BPF set is of more fundamental nature than the DUSF set. It has been shown that the operational matrices for integration in both the domains are identical. Hence, function approximation and integration in these two domains always produce identical results. Finally, functional differential equations are solved using the stretch matrices in BPF as well as DUSF domains. Since, the set of BPF and DUSF are related through similarity transformation, the results obtained are identical. Three relevant numerical examples have been treated with supportive tables and figures. At the end of the chapter, seven study problems are included.
