Ivan - Since I regularly recommend your maths and physics books (and use and do research with Modelica)- very very interested in this. Good luck and please let us know when it can be pre-ordered.
Ah no, I'm very far from the "book draft" phase — I'm more at the "Hello world" stage ;) I've been scoping out the hands-on projects first (e.g. simulate electric motor, heater, AC unit, heatpump, etc). I think adding the ODE theory will be the easy part, so I'm focussing first on the real-world projects/applications, which might be interesting to release as standalone blog posts to make the company blog look alive https://minireference.com/blog/ ;)
Assuming you mean Simulink rather than Matlab its not quite a direct alternative. You can use Modelica and Simulink for modeling the same type of problems but they use different modeling approaches. Simulink uses cuasal modeling, where signals flow via connections between individual blocks, transmitting values of individual variables from the output of one block to inputs of another block. Modelica uses acuasal modeling - in Modelica, individual components of the model describe the equations directly and by interconnecting individual components, the systems of equations become connected.
If you are looking for a direct open source causal modeling alternative to Simulink, then SciCos (www.scicos.org) is worth a look. I would recommed playing with both Open Modelica and SciCos to see which is the best fit for you.
https://www.openmodelica.org/
Ivan - Since I regularly recommend your maths and physics books (and use and do research with Modelica)- very very interested in this. Good luck and please let us know when it can be pre-ordered.