Then Comes the Train Wreck

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Differential equations is one of the worst taught math courses.

It typically starts off fine:

• separation of variables,
• integrating factors,
• characteristic polynomials.

And then comes the train wreck.

The train wreck:

The instructor skips ahead to their favorite area of research.

Except they’ve barely covered the foundations.

Whole branches of foundational material got skipped.

Numerical methods?

Laplace transforms?

What are those??!

It’s like the blind men feeling different parts of the elephant.

Depending on who their instructor is, different students leave with a different idea of what the course is.

Further reading: The funny thing about Differential Equations is that pretty much everyone who teaches it has a different conception of what it covers. .

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