An Extension to an Algebraic Method for Linear Time-Invariant System and Network Theory: The full AC-Calculus

Details An Extension to an Algebraic Method for Linear Time-Invariant System and Network Theory: The full AC-Calculus An Extension to an Algebraic Method for Linear Time-Invariant System and Network Theory: The full AC-Calculus

2007-09-19

arxiv.org/abs/0709.2935v1

Proceedings of the Fifth International Workshop on Symbolic Methods and Applications in Circuit Design, SMACD '98, Kaiserslaut

Mathematics

Classical Analysis and ODEs

V1: documentclass IEEEtran, 6 pages, 1 figure. Re-release of the printed version, with some minor typographical errors correct

Scientific paper

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.

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