A state-space procedure for solving linear dynamic systems by the 'walsh series is developed. A new operational mat.ri x plays the main role and a new Kronecker product formula is established. The laborious use of Corrington's tables is eliminated. SevernI examples illustrate the process and demonstrate the power of the approach.

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In non-linear systems analysis, multiple dimensional Laplace transform is often applied in solving the voltcrra model. Tho special technique for the inverse Laplaco transform solution is called thc association ol variables. Throe new theorems are developed for the theory of association. Compared with the inspection method of Brilliant, the pair listing method of Lubbock, the new approach is much simpler and easier and more systematic. Several illusLrative examples are included.

The nnnlyt.ic mot.hods for evaluating the time response of irrational transfer fuuct.iona are incomplete. The graphical approaches for solving the problem ure inaccurate. This paper et.tompte to attack the general inverse Laplace transform problem under the now light shed by the Fast Fourier transform. An algorithm for t.he inverse Laplace t.rnnsforrn is developed. Several typical but difficult, cases arc st.udied and the results arc extraordinarily snt.isfuct.ory.