Publication Date
Spring 4-15-2015
School
College of Arts and Sciences
Major
Mathematics
Keywords
Symmetry, Differential Forms, Lie Groups, ODE, Lie Derivative, Group, Differential Equations, Ordinary Differential Equations, Ordinary
Disciplines
Algebra | Geometry and Topology | Ordinary Differential Equations and Applied Dynamics | Other Mathematics
Recommended Citation
Shumate, Richard M., "Solving Ordinary Differential Equations Using Differential Forms and Lie Groups" (2015). Senior Honors Theses. 488.
https://digitalcommons.liberty.edu/honors/488
Abstract
Differential equations have bearing on practically every scientific field. Though they are prevalent in nature, they can be challenging to solve. Most of the work done in differential equations is dependent on the use of many methods to solve particular types of equations. Sophus Lie proposed a modern method of solving ordinary differential equations in the 19th century along with a coordinate free variation of finding the infinitesimal generator by combining the influential work of Élie Cartan among others in the field of differential geometry. The driving idea behind using symmetries to solve differential equations is that there exists a coordinate system for any given differential equation such that the equation can be directly integrated within the newfound system.
Included in
Algebra Commons, Geometry and Topology Commons, Ordinary Differential Equations and Applied Dynamics Commons, Other Mathematics Commons
