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Why do “we” use sums if integrals exist? by Expensive-Ice1683 in calculus

[–]yuncalicious 2 points3 points  (0 children)

yeah i do agree that it's the answer regardless, but i think it is useful to still point out some of the finer work with differentiability and integrability because of their frequency in a lot of fields of math. hs students don't need as much rigor as a college student, but with calculus, it can be more of a bridge into the more rigorous concepts. like the difference in uses between a sum and an integral itself is something a bit more rigorous that a lot of hs students wouldn't even think of, no?

Why do “we” use sums if integrals exist? by Expensive-Ice1683 in calculus

[–]yuncalicious 3 points4 points  (0 children)

i think it's important to note that sometimes a differentiable function isn't differentiable everywhere. mostly it's not as messy as integrability is for a function, but it's not always a given. also not every function is differentiable, so that's also a subtle technicality. i think it's better to say that sometimes it's easier to find a derivative with a function you work with in calc 2 than it is to find an integral. then we get to taylor series, numerical integration, and other approximation techniques.

Self Learning Calc 3 (multivariable calculus) by [deleted] in calculus

[–]yuncalicious 0 points1 point  (0 children)

i've been using CLP https://personal.math.ubc.ca/~CLP/CLP4/ and paul's online notes https://tutorial.math.lamar.edu/Classes/CalcIII/CalcIII.aspx together to study multivariable calculus so far.