What class will I start to study these?
From my experience you probably wont ever approach them from a 'teaching' point of view. I have come across them while doing some computer simulations and having to solve them numerically but that's it. I've taken the full calculus stream at my university and they never came up once.
If you're really interested in learning about them maybe there's a pure math course that deals with them. Otherwise just find a textbook and learn them yourself.
These first appeared to me in Classical Mechanics 1. In particular, when we were studying oscillations.
I, too, ran into them in a Classical Mechanics course and possibly other courses.
I'm a math major currently at UW and am just beginning to study abstract algebra and topology this quarter. Thus far I've taken almost every junior level math course at my school and elliptic integrals have only been mentioned in my introduction to real analysis class, however, I would not classify this encounter as learning about them.
My friend told me he met them in Electromagnetism. I've found them in Classical Mechanics and in a numerical analysis exam.
I saw these in three classes at jr/sr level in US:
classical mechanics - just like everyone else
applied complex analysis - Schwarz-Christoffel conformal transformations often yield elliptic integrals. The class also spent a week on elliptic functions; elliptic integrals are inverse elliptic functions.
It is easy to conceive of versions of these classes that do not cover elliptic integrals at all; whether or not a course includes them has nothing to do with the "level" of the course, it is simply a matter of taste on the part of the professor/department. In my experience, once you know calculus pretty well you can learn most of what you need about special functions on your own. Knowing complex analysis can greatly help in some cases, but if you don't know it I wouldn't let that stop you.
the standard references are Abramowitz and Stegun:
and Whittaker and Watson:
Wolfram Mathworld and Wikipedia are often quite good, too.
Thanks everyone. We're studying Simple Harmonic Motion and Damped Harmonic Motion and it was (very) briefly referenced in the lecture so I got curious.
Sometimes courses in "special functions", Bessel functions, etc., deal also with elliptic functions but one cannot guarentee that such a course will cover them.
My Calc II prof mentioned that one of the 3rd or 4th year numerical methods courses in the applied math dept. covered that sort of thing. I think they tend to do more of a general unit on those integrals that don't work out 'nicely' rather than specifically looking at elliptic integrals though.
When Mathematica spits one out as the answer to some problem.
Well, one thing I've been curious about is what would happen if a student who is learning about conic sections in precalculus just happened to ask what the circumference of an ellipse was.
Now, I myself have too much of a history of asking questions that are revealing of my knowledge of higher mathematics which can often bother my teacher, so I would be overly suspect of "derailing the curriculum" or whatever.
Anyways, it is my belief that Elliptic integrals seem to come up commonly in arc lengths, possibly due to something involving square roots.
I am still trying to learn about Elliptic integrals and functions, but it all seems too advanced for me.
So I think I should wait until I'm a pro at Integration. Knowledge of Elliptic Functions probably can give you an upper hand in manual Integration contests.
I do sort of understand the Elliptic Curve group stuff though.
Wrong units for circumference. This is an area...
Oops. You're right.
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