Intro to Differential Equations

This course offers a thorough study of differential equations and their applications, starting with first-order equations used to model physical systems. It covers second-order linear equations for oscillations and circuits, as well as eigenvalues and eigenvectors for solving systems of equations and analyzing stability. Students will explore systems of first-order equations and the stability of nonlinear autonomous systems, with applications in fields like fluid dynamics. Fourier series are introduced for periodic functions, and separation of variables is applied to solve partial differential equations, addressing problems in heat diffusion and mechanical vibrations.