#### Date of Final Oral Examination (Defense)

8-2010

#### Type of Culminating Activity

Thesis - Boise State University Access Only

#### Degree Title

Master of Science in Mathematics

#### Department

Mathematics

#### Major Advisor

Rama Mishra, Ph.D.

#### Abstract

This thesis discusses the basic tools required to understand the new Galois theory that has been developed in the setup of differential equations. Since the classical Galois theory for polynomial equations is very well known and is handy for the solvability criteria for polynomial equations, it is believed that the differential Galois theory turns out to be equally useful in the theory of differential equations. In this thesis, we show the similarities and the differences between the polynomial and the differential Galois theories, and explain the fundamental theorem of differential Galois theory. In order to apply this theory, one needs to find the differential Galois group of a given differential equation. Therefore, we compute the Differential Galois group of a few differential equations and verify the solvability issue of those differential equations.

#### Recommended Citation

Eghbali, Soheila, "Galois Theory for Differential Equations" (2010). *Boise State University Theses and Dissertations.* Paper 145.

http://scholarworks.boisestate.edu/td/145