1. The problem is to understand what a PDE is. 2. PDE stands for Partial Differential Equation. 3. A PDE is an equation that involves partial derivatives of a function of several variables. 4. It is used to describe phenomena such as heat, sound, fluid flow, elasticity, and quantum mechanics. 5. The general form involves unknown functions and their partial derivatives, for example: $$\frac{\partial u}{\partial t} = k \frac{\partial^2 u}{\partial x^2}$$ which is the heat equation. 6. Important rules: PDEs involve derivatives with respect to more than one independent variable. 7. Solving PDEs often requires boundary and initial conditions. 8. PDEs are fundamental in physics and engineering to model continuous systems.