Hmm, sort of? I can't really generalize from my own (first year, before joining a lab full-time) PhD courses, but I found them challenging in a way that differed from undergrad: more expectation that you'd be able to figure out the solutions to the hard problems by learning entire new fields on the fly.
Completely depends on the program of study and school. In astronomy and physics programs, graduate courses are far more advanced, but grades are based almost entirely on homework sets. Undergraduate course are less comprehensive, but have a mix of homework and tests. Working on problem sets is chronically hard, while tests are acutely hard.
I mean that PhD candidates would be the primary target, rather than undergraduates, although talented, advanced undergraduates would also be welcome (this being Caltech, I'd expected there to be plenty of juniors and seniors in the course).
I say this because it drops into diffeqs and fairly subtle/complex behavior quickly.
I TA'd BE/CS/CNS/Bi/etc 191 years ago, we had some freshman in the class, and there was definitely the expectation they'd have some familiarity with differential equations; for example, the mass-action model of chemical reaction networks relies on them.
These sorts of classes tend to get students in a broad range of levels, and I think there's the expectation that they'll figure out whatever they're unfamiliar with. I doubt this class is targeted to graduate students, but Caltech classes tend not to have a graduate/undergraduate distinction.
I'm hoping this is a typo '191 years ago'. Don't mean to sound pedantic just interested when this was. My friend was in Caltech for his MS + PhD in Electrical engineering from 2008 onwards. I think he graduated in 2014-ish.
difeq is part of the common core that everyone must take to graduate and taught to sophomores first term, although a few (maybe 10-15 or so each year? out of about 200-250) (as of about a decade ago) students will test out of ma1a and then take ma2a first term freshman year instead of sophomore year. Testing out of ma1a requires knowing both calculus and also proof techniques.
courses numbered 100-199 are taken by both undergrads and graduate students, and because of Caltech's "rigorous" core often (but not always) the undergrads have an easier time.
I don't know this class specifically, but you would probably have a couple super motivated sophomores but mostly juniors and seniors taking a course numbered like this. Occasionally a few people will take 100-level courses freshman year (I took one such full-year and 1 one-term class, and I wasn't the only frosh in either).
(humanities/social science courses numbered 100+ are a bit of a different matter and tend to be super easy, but no one really takes those classes seriously for obvious reasons)
No, typically things end at single variable calculus, although it depends on the school. I can't imagine that there is much value to having high school students doing diff eq.
At Caltech specifically FWIW, the biology major requirements include intro to diff eq (Ma 2),[0] which is usually taken in the first quarter of sophomore year.
yes but caltech is atypical (at many schools, biologists would fail diff eq just like many biologists fail organic chemistry). This course is definitely designed for educated, motivated students.
"Advanced undergraduate" or "beginning graduate." It's Caltech though so the distinction is a bit meaningless.