The operational matrices of integration and differentiation for the Fourier sine-cosine and exponential series

Abstract
For the Fourier sine-cosine series basis vector phi (t) and the Fourier exponential series basis vector psi (t), a linear nonsingular tranformation T is determined such that psi (t) equals T phi (t). This result is then used to show that the operational matrices of integration P and Q for phi (t) and psi (t), respectively, are related by the expression TP equals QT. Analogous results are derived for the corresponding operational matrices of differentiation D and R. General expressions are derived for T, P, Q, D, and R

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