Are there any really good resources on modelling with differential equations?

[matqkks]

I will have to teach a first course in differential equations. A good motivator might be to promulgate modelling with differential equations but I have seen some teachers have made polemic against modelling. Are there any really good resources on modelling with differential equations? I want something which will have an impact and motivate the learner. I am not really looking for artificial engineering examples but some bona fide real applications.
Also would like to bring in some history of differential equations.

 

[Philip Koeck]

I will have to teach a first course in differential equations. A good motivator might be to promulgate modelling with differential equations but I have seen some teachers have made polemic against modelling. Are there any really good resources on modelling with differential equations? I want something which will have an impact and motivate the learner. I am not really looking for artificial engineering examples but some bona fide real applications.
Also would like to bring in some history of differential equations.

Charging and discharging of a capacitor comes to mind.
Also chemical kinetics and radioactive decay.

See also https://www.researchgate.net/publication/333479286_Differential_equations_for_thermal_processes
for examples involving heat transport and gas pressure.

 

[fresh_42]

Here is my point of view:
https://www.physicsforums.com/insights/differential-equation-systems-and-nature/

Lotka-Volterra is the standard example because it is non-trivial and can be drawn. Maybe you like some of the many references I attached.

 

[Will Flannery]

Yes, my book .... Mathematical Modeling and Computational Calculus
See also ...
The Coming Revolution in Physics Education
A Revolution in Physics Education Was Forecast in 1989, Why Hasn't It Happened? What Will It Take?
A New Curriculum for Classical Physics

 

[gmax137]

What do you mean by modeling?

In my experience, modeling is synonymous with simulation, and was always real world applications, solved numerically.

This goes way beyond simple analytically tractible scenarios like tank concentration etc.

 

[Haborix]

Outside of modeling trivial systems, it usually requires a lot of subject matter knowledge to actually build-up a good model. For example, to generate a climate model, i.e., identifying the right variables and putting them in the right relationship to each other, would require subject matter knowledge in climate science beyond the student (and probably the lecturer). Common practice in a course on differential equations is probably to give a few examples of differential equations which model some system. Deriving those models is really the business of another field.

I don't interpret modeling to be synonymous with simulation. I was always annoyed with teachers who added numerical schemes into core courses. Felt like a waste of my time and their expertise.