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Cake day: June 12th, 2023

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  • Kogasa@programming.devtoMemes@lemmy.mlMath
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    13 days ago

    Stokes’ theorem. Almost the same thing as the high school one. It generalizes the fundamental theorem of calculus to arbitrary smooth manifolds. In the case that M is the interval [a, x] and ω is the differential 1-form f(t)dt on M, one has dω = f’(t)dt and ∂M is the oriented tuple {+x, -a}. Integrating f(t)dt over a finite set of oriented points is the same as evaluating at each point and summing, with negatively-oriented points getting a negative sign. Then Stokes’ theorem as written says that f(x) - f(a) = integral from a to x of f’(t) dt.













  • All cloud providers will support budget notifications. That doesn’t do much good when you shoot past the budget in a short timespan. I set a Google cloud budget of $20/month and enabled a Tensorboard instance, which had no observable indication that it cost anything except the base cost of the VM, and got notified that I was $280 over budget the next day. Apparently there was an upfront $300/month/user fee for Tensorboard. (Several months later they changed the pricing model to $10 GiB/month with no user fee.)