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.
https://openworks.wooster.edu/independentstudy/949
Disciplines
Applied Mathematics
Publication Date
2013
Degree Granted
Bachelor of Arts
Document Type
Senior Independent Study Thesis Exemplar
Included in
© Copyright 2013 Ruth A. Steinhour