/sci/ - Science & Math

anyone have any particularly good youtube vids to recommend for learning basic calculus. Looking to supplement my reading with lectures. I know of 3 blue 1 brown as well as Strang's lectures too. Seems there are a bunch but I'd rather not sift through all of them. I'm a beginner (if that wasn't clear). Thanks in advance.

>>10629396
We don't integrate with rectangles. We integrate with tangential slopes at every conceivable point. It's a fundamental aspect of calculus. For finite sums, many different methods are applied, including the trapezoid rule, which you suggested. This value can also be found by using both left and right values at the top of the rectangles, then averaging the two results. The reason we use rectangles is because, as the width of the rectangle approaches zero, it forms a single value, rather than two different values. An infinite sum of these infinitesimally small single values provides the most accurate sum.

We don't worry about minimizing the gap, because the limit already approaches zero. Just imagine cutting the rectangles into smaller rectangles. The distance between the two upper corners of the rectangles approach zero.

It's important to remember that everything in calculus is fundamentally based on the infinitesimal, which is the essence of limits.