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Results tagged with integration
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user 4362
Questions related to various forms of integration including the Riemann integral, Lebesgue integral, Riemann–Stieltjes integral, double integrals, line integrals, contour integrals, surface integrals, integrals of differential forms, ...
3
votes
2
answers
395
views
Integration in several variables and elementary applications
This fall I'm teaching the "second half" of the standard entry-level undergraduate multivariable calculus course: the focus is on double and triple integrals, path integrals, Green's theorem, Stokes' …
32
votes
6
answers
3k
views
Can distribution theory be developed Riemann-free?
I imagine most people who frequent MO have been indoctrinated into the point of view that the Riemann integral can be safely discarded once one has taken the time to develop the Lebesgue integral. Af …
- 29.2k
135
votes
Why should one still teach Riemann integration?
From a conceptual standpoint, I think that there are three things one asks of an approach to integration
1) An easily accessible geometric interpretation
2) A readily available computational toolbox … I can't even imagine how one builds integration in higher dimensions from the Cauchy point of view, short of turning Fubini's theorem into a definition. …
16
votes
Integrals from a non-analytic point of view
I think this point of view on integration - as a pairing between homology and cohomology - leads to many of the genuinely non-analytic formulations of integration. … Here is what I think integration is all about. …
- 29.2k