llamaz 1 hour ago [-]
I think the calculus of variations might be a better approach to introducing ODEs in first year.
You can show that by generalizing calculus so the values are functions rather than real numbers, then trying to find a max/min using the functional version of , you end up with an ODE (viz. the Euler-Lagrange equation).
This also motivates Lagrange multipliers which are usually taught around the same time as ODEs. They are similar to the Hamiltonian, which is a synonym for energy and is derived from the Euler-Lagrange equations of a system.
Of course you would brush over most of this mechanics stuff in a single lecture (60 min). But now you’ve motivated ODEs and given the students a reason to solve ODEs with constant coefficients.
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2019.10.02 Wednesday ACHK