unless it's an honors course,instead, one gives rough ideas as to where this or that formula comes from, why one shouldn't be surprised at certain outcomes, and where to be careful. (also, examples are very useful, in order to emphasise certain points.)
or if you want to gain the ire of your students.
i've heard it said that "a calculνs course is not a mathematιcs course.
whether you agree or disagree, a ca1cu1us course isn't a theoretical maths course, just as $tats 101 isn't a theoretical statistιcs course.
one's studies must begin somewhere, you know.
i've never taught a theoretical maths course before.
i'm curious what it's like ..
.. but not so curious as to teach one, right away. there are papers to write and more research to do, after all!
2 comments:
I'd rather think of "real" calculus (e.g. for math/sci/eng majors) as a math/sci/eng course, rather than watered down real analysis. Which is why I like to justify the curvature formula by going through a=v^2/r from physics, or to introduce cylindrical and spherical coordinates through industrial robots.
www.ifr.org/modules.php?name=News&file=article&sid=15
The instructions I was given for teaching our Engineering Calculus courses was basically "give them no proofs, do lots of examples and just give them the formulas". The "regular" calculus classes (science/math/engineers (!?!!)) is close to that also. Lots of handwaving, etc. An example via robots would be entirely lost on them, and doing such examples too often would result in negative evaluations, along the lines of "Talked about stuff that wasn't on the exam. Needs to do more examples." Of course, the exams are literally homework problems, they know that they will be old homework problems and still at least a third of the class fails miserably.
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