Re:What are Differential Equations and how do they work?
by enriquto on Sunday October 04, 2020 @03:03PM
(#24681448)
> The most important skill in this area is ability to compose differential equation from the description of the problem.
This is called "modeling", and together with analysis and simulation is one of the three main parts of the theory. Where did you study differential equations? From my experience, it is typically taught that way, at least in the european universities that I know. Even in the most hard-core mathematics departments they may focus strongly on the analysis part (existence, uniqueness, regularity) to the detriment of a bit of modeling or simulation; but I have never seen those hidden. The "algebraic" solution of the equations is a fringe subject that is most often omitted, (except when it leads to a simple analysis, e.g. linear equations).
Re:What are Differential Equations and how do they work?
by d_silin on Sunday October 04, 2020 @03:38PM
(#24681690)
In UK. We definitely spent a lot of time solving DEs of various classes, and very little on "modelling" part. But I remember that numerical methods were covered pretty well too.
This is called "modeling", and together with analysis and simulation is one of the three main parts of the theory. Where did you study differential equations? From my experience, it is typically taught that way, at least in the european universities that I know. Even in the most hard-core mathematics departments they may focus strongly on the analysis part (existence, uniqueness, regularity) to the detriment of a bit of modeling or simulation; but I have never seen those hidden. The "algebraic" solution of the equations is a fringe subject that is most often omitted, (except when it leads to a simple analysis, e.g. linear equations).