Differential Equations I – Graduate Course
This course is designed to provide students with fundamental understanding of ordinary differential equations and some of the applications in engineering and applied sciences, differential equations can be used to model and understand the behavior of a system. The emphasis is on developing the mathematical properties and solution methods that characterize ordinary differential equations, including a more detailed examination of eigenvalues and eigenvectors, stability, the phase plane. In addition:
- Working with systems of ordinary differential equations and non-linear ordinary differential equations is also stressed.
- Developing and understanding and appreciation of the qualitative behavior of the solution vis-à-vis orbits and phase plane portraits;
- Being able to formulate and find solutions to more complex mathematical problems encountered in the applied sciences and engineering involving differential equations. Theory and analysis is stressed throughout, however the course also requires that the student develop proficiency in working with solution methods for ODEs that are covered in the text.
