Computational Algebraic Analysis for Systems of Linear Constant Coefficients Differential Equations

Abstract

In this section we provide the background on those aspects of algebraic analysis which will be necessary in the rest of the book. Historically we believe that Euler was the first major mathematician to use the term “algebraic analysis” in connection with his important work on general solutions to linear ordinary differential equations with constant coefficients, [71]. Currently, the term “algebraic analysis” refers to the work of the Japanese school of Kyoto (Sato, Kashiwara, Kawai, and their coworkers) which founded and developed methods to analyze algebraically systems of line partial differential equations with real analytic coefficients [102]. Their results, however, rest on some preliminary work, in which algebra was used to study general properties of systems of linear differential equations with constant coefficient.