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This paper is divided into two parts. The first part traces (in details providing proofs and examples) the history of the solutions of polynomial equations(of the first, second, third, and fourth degree) by radicals from Babylonian times (2000 B.C.) through 20th century. Also it is shown that there is no solution by radicals for the quintic (fifth degree) and higher degree equations. The second part of this thesis illustrates both numerical and graphical solutions of the quintic and higher degree polynomial equations using modern technology such as graphics calculators (TI-85, and HP-48G) and software packages (Matlab, Mathematica, and Maple). / Graduation date: 1995

A new method for transient simulation of integrated circuits has been developed and investigated. The method utilizes expansion of circuit variables into Chebyshev series. A prototype computer simulation program based on this technique has been implemented and applied in the transient simulation of several MOS circuits. The results have been compared with those generated by SPICE. The method has been also combined with the waveform relaxation technique. Several algorithms were developed using the Gauss-Seidel and Gauss-Jacobi iterative procedures. The algorithms based on the Gauss-Seidel iterative procedure were implemented in the prototype software. They offer substantial CPU time savings in comparison with SPICE without compromising the accuracy of solutions. A description of the prototype computer simulation program and a summary of the results of simulation experiments are included.