You know the missing mathematical background isn't actually that hard to learn. And once you learn it, you may notice important details you're currently missing.
For instance the lecture you got annoyed with was covering how to correctly model a second degree differential equation. So you know that d^2x/dx^2 = f(x, u). This is a different and more complicated problem than a first order differential equation. They handled it by turning it into a system of first order differential equations. And then demonstrated how the obvious way to do it lead to numerical instability, creating a physically incorrect result. And then they had to do more complex stuff to avoid the numerical instability.
The underlying concepts share a lot with a simple first order equation. But the generality is letting you tackle and deal with issues that a simple model can't. Plus the technique described can be expanded in a straightforward way to model a combination of interacting things.
But you froze up at the idea of linear algebra and didn't even realize that they were dealing with a much more complicated problem than you thought.
It could be easier to understand if instead using z-Transform they shown that you could do better numerical second order integration if you take few previous points into account instead of just one as in naive method of integrating twice with forward Euler integration.
Of course purpose of this lecture was probably not to make you understand what you are actually doing while numerically integrating, just to teach you how to put this stuff into simulink that has z-Transform as one of it's primitive building blocks.
I did just fine, thank you. Matrix form is not necessary to tell me that we need to approximate both x and dx/dt in order to use our knowledge of d^2x/dt^2. It is not particularly difficult to remember that the second derivative is the first derivative of the first derivative.
For instance the lecture you got annoyed with was covering how to correctly model a second degree differential equation. So you know that d^2x/dx^2 = f(x, u). This is a different and more complicated problem than a first order differential equation. They handled it by turning it into a system of first order differential equations. And then demonstrated how the obvious way to do it lead to numerical instability, creating a physically incorrect result. And then they had to do more complex stuff to avoid the numerical instability.
The underlying concepts share a lot with a simple first order equation. But the generality is letting you tackle and deal with issues that a simple model can't. Plus the technique described can be expanded in a straightforward way to model a combination of interacting things.
But you froze up at the idea of linear algebra and didn't even realize that they were dealing with a much more complicated problem than you thought.