Applied Ordinary Differential Equations with Theory

This course provides a comprehensive introduction to ordinary differential equations, their applications, and their theoretical underpinnings. During the course, we will see how applied mathematicians use ordinary differential equations to solve practical applications, from understanding the underlying problem, creating a differential-equations model, solving it using analytical, numerical, or qualitative methods, and interpreting the findings in terms of the original problem. We will also learn about the underlying rigorous theoretical foundations of differential equations and the mathematical formalism used to establish this theory. Prerequisites: Multivariable calculus; Linear algebra.