Differential Equations

Catalog description

This course focuses on Differential Equations and Computational Methods. It is intended for Mathematics and Science students who are going to apply these techniques in their coursework. Reflecting the shift in emphasis from traditional methods to new computer-based methods, we focus on the mathematical modeling of real-world phenomena as the goal for the study of differential equations. Topics covered include standard methods for 1st order equations (separation of variables, integrating factor for linear equation, etc.), population models, equilibrium and stability, acceleration-velocity models, numerical methods, Euler, Improved Euler, Runge-Kutta, linear equations of higher order, resonance in mechanical and electrical systems, systems of ODEs eigenvalues and numerical methods; nonlinear systems with applications to population modeling and nonlinear mechanics, chaos, and Laplace transform techniques.