Richard Feynman’s Integral Trick (2018)
A lot of undergraduate math programs in the US start with unnecessarily hard calculus classes &quot;weed-outs&quot; which is unfortunate, since it discourages students who might have pursued mathematics otherwise. I can say from personal experience that Calculus II was my worst math grade, I fared much better in rigorous and challenging classes like real analysis or differential topology. To do well in elementary calculus one has to seemingly practice integration techniques in various permutations for hours, and honestly for what future purpose I cannot say.<p>EDIT: I finally understood calculus after taking introduction to real analysis, and it was amazing because for the first time all the hand-waving disappeared and could be replaced with rock-solid arguments and increasing levels of abstraction (starting from the very definition of what the real numbers are). This is also important because functions can get very pathological[0][1][2]<p>[0] <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Weierstrass_function" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Weierstrass_function</a> (continuous everywhere but differentiable nowhere)<p>[1] <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Cantor_function" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Cantor_function</a> (derivative is zero almost everywhere but f(x) goes from 0 to 1)<p>[2] <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Thomae&#x27;s_function" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Thomae&#x27;s_function</a> (continuous at irrationals but discontinuous on rationals)