A Second Course in Differential Equations
Delve into advanced topics in ordinary differential equations through this comprehensive 5-hour course. Explore linear systems, solution set independence, eigenvalues, and eigenvectors. Master the matrix format of linear differential equation systems and tackle example problems involving the Wronskian. Study repeated real eigenvalues, complex eigenvalues, and notation changes. Learn to solve nonhomogeneous linear systems using undetermined coefficients and variation of parameters methods. Discover numerical methods, including the Euler method and its improvements, as well as the fourth-order Runge-Kutta method. Gain practical skills in using Python for numerical calculations, from installation to constructing code for various formulas. Apply these techniques to solve second-order ODEs, systems of first-order ODEs, and higher-order ODEs. Conclude with an exploration of plane autonomous systems and their applications through example problems.