ALGEBRAIC THEORY OF DIFFERENTIAL EQUATIONS

Abstract

My project topic explains how to look a polynomial coefficient linear differential equations in an algebraic environment. While differential equations are commonly considered to belong to the world of analysis, algebra has a lot of interesting things to say about differential equations and their solutions. The algebraic theory of linear differential equations serves as an analogue to ”The classical Galois theory for polynomial equations”. In this context, a differential field, comprising a field F (having characteristic 0) equipped with a derivation akin to the differentiation in R or C, plays a central role. So basically differentiation can be seen as a homomorphism point of view and consequently we can apply algebraic properties on differentiation.