Review of vectors functions by going over a concept check and true-false quiz at the end of the Stewart Calculus chapter

In this video, I go through obtaining the vector equation of a tangent line to a space curve, by replacing the parallel vector with the tangent vector from the general vector equation of a line. This was

Tutorial on obtaining the tangent vector, unit tangent vector, and equation of the tangent line to a space curve.

In this video, I go over the concept check review from the end of the vector functions chapter in my calculus book. I cover vector functions, space curves, their derivatives & integrals, curvature,

Concept check review tutorial from the end of the vector functions chapter in my Stewart Calculus book.

In this video, I go over the concept check questions and true-false quiz as part of the review on the vector functions chapter from my calculus book. There are 9 concept check questions and 14 quiz questions,

In this video, I go over Theorem 2, which states that we can move a constant out of the sum of a series as well as add or subtract series individually. These follow from the Limit Laws of Sequences, and

Tutorial on Theorem 2 for infinite series, which says that convergent series can be added or subtracted.

In this video, I go over Theorem 1, which states that the terms of a convergent series approach zero. Conversely, if the terms don't approach zero, the series diverges, hence providing a useful test for

Tutorial on a convergence theorem for infinite series, and what follows from it is the Test for Divergence.

In this video, I show that the harmonic series, 1 + 1/2 + 1/3 + 1/4 + ..., diverges by showing its even power partial sums are greater than a similar but smaller series involving repeating 1/2 terms. This

In this video, I go over an infinite series in which arises an example of the famous telescoping sum such that all the terms of the series cancel except for the first and last term. The telescoping sum

Example of a series whose sum can be determined by using the telescoping sum and partial fraction decomposition.

In this video, I show that the infinite series xn = x0 + x1 + x2 + ... is just a geometric series, and converges if the absolute value of x is less than 1. By common convention, x0 = 1, so the first term

Example on finding the sum of the infinite series x^n where |x| < 1 by noticing it is a convergent geometric series.

In this video, I go over an example of converting the number 2.3171717... (with infinite repeating 17) into a fraction by writing the repeating 17s as an infinite geometric series with common ratio 1/100,

Example on converting a number with repeating digits into a fraction of integers via the geometric series.

In this video, I go over two examples and two methods of identifying if a series is a geometric series, and then finding its sum if it converges. In the first example, we are given the first 4 terms of

Two examples on identifying geometric series and finding their sums, if the series converges.

In this video, I go over the geometric series, which is the sum a + a r + a r^2 + ..., and show that if the absolute value of the common ratio r is less than 1, then the sum is just the first term divided