#### Abstract

Differential equations are vitally important in numerous scientific fields. Oftentimes, they are quite challenging to solve. This Independent Study examines one method for solving differential equations. Norwegian mathematician Sophus Lie developed this method, which uses groups of symmetries, called Lie groups. These symmetries map one solution curve to another. They can be used to determine a canonical coordinate system for a given differential equation. Writing the differential equation in terms of a different coordinate system can make the equation simpler to solve. This I.S. explores techniques for finding a canonical coordinate system and using it to solve a given differential equation. Several examples are presented.

#### Advisor

Bowen, Jennifer

#### Second Advisor

Wooster, Robert

#### Department

Mathematics

#### Recommended Citation

Steinhour, Ruth A., "The Truth About Lie Symmetries: Solving Differential Equations With Symmetry Methods" (2013). *Senior Independent Study Theses.* Paper 949.

http://openworks.wooster.edu/independentstudy/949

#### Disciplines

Applied Mathematics

#### Publication Date

2013

#### Degree Granted

Bachelor of Arts

#### Document Type

Senior Independent Study Thesis Exemplar

© Copyright 2013 Ruth A. Steinhour