Five hour deep-dive into 7 advanced math problems on vector functions. Buckle up!

In this video, I go over the end-of-chapter Problems Plus questions and solve 7 very advanced problems on vector functions. Three of the questions involve launching a projectile either on a flat, inclined,

Livestream discussion on electromotive force (emf) and electromagnetism in general.

In this video, I show that modifying our earlier Theorem 2 remainder estimate by adding the partial sum to both sides of the inequality provides a much better approximation than simply using the partial

Tutorial on approximating the sum of infinite series by using an interval via the remainder estimation theorem rather than just the partial sum.

Remainder Estimate for the Integral Test + Example & In this video, I approximate the accuracy of the partial sums of a series that converges via the Integral Test by estimating the size of the remainder.

Tutorial on estimating the accuracy of a series by establishing the remainder estimation theorem for the integral test.

In this video, I show that the sum of the series with terms (ln n) / n diverges to infinity by computing its corresponding improper integral via the Integral Test. First noting that the natural logarithm

Tutorial on showing that the series with terms natural log of n divided by n diverges to infinity via the Integral Test.

Livestream answering math and science questions, as well as examining Faraday's Flux Rule for electrical circuits.

In this video, I use the Integral Test to show that the p-series, whose terms are 1/n^p, is convergent if p is greater than 1 and divergent for all other values of p. When p is less than 0, the terms approach

Tutorial showing the values of p in which the p-series converges and diverges, which I show using the Integral Test.

In this video, I go over the Integral Test, which states that a series converges only if its corresponding improper integral also converges. Likewise, if the improper integral diverges, then the series

Tutorial on the Integral Test for determining if an infinite series converges or diverges, including an example.

In this video, I go over an introduction into estimating sums of series by examining whether their corresponding improper integrals converge or diverge, thus providing the basis for the Integral Test.

Tutorial going over an introduction into estimating the sums of series by examining their corresponding improper integrals.

In this video, I show that the sum of diameters of an infinite number of circles contacting between two big circles sums to the radius of the bigger circles, thus providing a geometric interpretation of

Tutorial showing the sum of diameters of an infinite sequence of circles contacting two bigger circles provides a geometric interpretation of the series with terms 1/(n(n+1)).

In this video, I show that the sum of differences between successive positive integer powers x^n for 0 ≤ x ≤ 1 can be written as an infinite series, and the resulting sum is equal to 1 or the unit square.

Tutorial on showing the geometric interpretation of a previously covered series as a sum of differences of curves x^n.