English

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.

Keywords

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

R2 v1 2026-06-21T09:18:55.767Z