I would like to know, in general, how events can be modeled by differential equations. Recently, I have learned how to solve some PDEs, but it is not enough. I want to know how the Heat Equation was "created", for example.
Let's suppose the following scenario:
I want to know the volume of blood ($b$) that flows through my veins depending on time ($t$), and how fast my heart beats ($h$). How could I model this? Just throw some partial derivatives and constants ($k_n$) and that's it? For example,
$$\partial^2_b = 2t \partial_t + \partial_h + k_0 + error$$
I would really appreciate anything as an answer, either a general or particular explanation.
Thanks.