Introduction
What Are Differential Equations Anyway?
This lecture introduces the subject with Newton’s Law of Cooling $$ \frac{\mathrm{d} u}{\mathrm{~d} t}=-K\left(u(t)-T_{0}\right), $$ where $u=u(t)$ denotes the temperature of an object at time $t$ in an environment with constant ambient temperature $T_0$. Many notions that will appear in the course are introduced. Examples are integral curves, initial-value problems, equilibrium states, and phase line analysis.
Full Set of Lecture Notes
The notes for this lecture are available here.