An Extension to an Algebraic Method for Linear Time-Invariant System and Network Theory: The full AC-Calculus
Classical Analysis and ODEs
2007-09-20 v1 Symbolic Computation
Abstract
Being inspired by phasor analysis in linear circuit theory, and its algebraic counterpart - the AC-(operational)-calculus for sinusoids developed by W. Marten and W. Mathis - we define a complex structure on several spaces of real-valued elementary functions. This is used to algebraize inhomogeneous linear ordinary differential equations with inhomogenities stemming from these spaces. Thus we deduce an effective method to calculate particular solutions of these ODEs in a purely algebraic way.
Cite
@article{arxiv.0709.2935,
title = {An Extension to an Algebraic Method for Linear Time-Invariant System and Network Theory: The full AC-Calculus},
author = {Eberhard H. -A. Gerbracht},
journal= {arXiv preprint arXiv:0709.2935},
year = {2007}
}
Comments
V1: documentclass IEEEtran, 6 pages, 1 figure. Re-release of the printed version, with some minor typographical errors corrected