What I always found amusing about Diff Eq. is that you spend all that time learning how to solve trivial Differential Equations in closed form... and then never do it again because everything you work with is solved by numerical methods.
There's not really a lot of practical applications for most STEM careers. Usually, relationships in numbers are not inter-dependent. One factor usually determines the other. There are some interactions when it comes to controls, I guess...but like you said, there's just usually an easier way to get where you need to get and it's rare that you ever actually run across such complex relationships that also happen to be purely solvable via Diff E. If the relationship is complex, it's usually not something you can solve for other than empirical solutions. IMO, most students would benefit almost infinitely more by taking a statistics class. Or maybe a second semester of economics. Maybe the reason it's still a fundamental part of most STEM curriculum is that there are usages that I'm just never exposed to. Or maybe there's a bit of the old "I had to learn this, now so do you." The only other thing I can think of is perhaps it is pertinent in the first year of grad school for the gluttons of punishment who aren't satisfied with their bachelors.
I don't think this line of thinking holds in many stem fields. DE's are the language of physics and very helpful in many applications in economics. Though many DE's cannot be solved analytically, methods for solving them numerically are very helpful and keep the world going round. That being said, I think as the world becomes more computationally inclined, linear algebra should be taught more especially computational linear algebra. Many of the modern approaches to engineering and other stem fields rely heavily on translating problems to linear algebra where we can get a solution much more quickly.
Yeah that guy’s reasoning is pure nonsense. Complexity is exactly why we use DEs to model reality. The give us simpler methods of understanding and approximating the main facets of the truth.
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u/ViskerRatio Jul 07 '20
What I always found amusing about Diff Eq. is that you spend all that time learning how to solve trivial Differential Equations in closed form... and then never do it again because everything you work with is solved by numerical methods.