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Examples Of Solving The Wave Equation In The Hyperbolic Plane, Cooper Ramsey
Examples Of Solving The Wave Equation In The Hyperbolic Plane, Cooper Ramsey
Senior Honors Theses
The complex numbers have proven themselves immensely useful in physics, mathematics, and engineering. One useful tool of the complex numbers is the method of conformal mapping which is used to solve various problems in physics and engineering that involved Laplace’s equation. Following the work done by Dr. James Cook, the complex numbers are replaced with associative real algebras. This paper focuses on another algebra, the hyperbolic numbers. A solution method like conformal mapping is developed with solutions to the one-dimensional wave equation. Applications of this solution method revolve around engineering and physics problems involving the propagation of waves. To conclude, …
Solving Ordinary Differential Equations Using Differential Forms And Lie Groups, Richard M. Shumate
Solving Ordinary Differential Equations Using Differential Forms And Lie Groups, Richard M. Shumate
Senior Honors Theses
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 …