Abstract: I was initially shocked by partial differential equations (PDEs).
The way I was taught involved complex physical models and laws. For a
student like me who just wanted to study the mathematics of these equations
(and how to solve them), the physical examples lead mainly to confusion. I
think it is much easier to understand pure, somewhat rigorous mathematical
analysis, than it is to learn both physics and math at the same time. These
notes are an attempt to explain linear PDE’s in mathematical terms. I try
to use geometrical intuition when possible. The notes were not written by a
mathematician or even a “math major”, so please read them critically.