So, I look at the sample demos of the Stanford EPGY online math courses. And the real analysis course. And behold - the explanations that you have to udnderstand look the same as the textbook of a standard calculus course. Besides, most college math courses take several quarters to complete, whereas Stanford EPGY only require one course for each (abstract alg, real analysis, etc..). So are the stanford EPGY math courses just brief versions of what you would get in a college math course? And would one of them ever count for credit for a state university one year sequence of say, abstract algebra or real analysis?
http://epgy.stanford.edu/courses/mat...15lecture.html
...Then again, explanations are supposed to simplify what the textbook is saying. So they tend to be more informal. Still, why not let the textbook be more informal itself?
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And why in the heck do they split up multivariable calculus into integral and differential???