A discussion of absolutely convergent series. Attention is given to why the terms of conditionally convergent series (those which are not absolutely convergent) can be rearranged to build new series that can converge to any desired number.

This video demonstrates how to build power series expansions of a number of functions by modifying the geometric power series in a number of ways. As a result, two fascinating infinite series are developed.

This video explains how to use the Ratio Test to determine the radius of convergence of a power series, and how to use this information to find the interval of convergence.

Rene Descartes invented the rectangular geometric coordinate system when he saw a rectangular grid pattern over his bed. This video begins with the geometric description of a parabola that would have been used by Euclid, and examines how we can use the genius of Descartes to provide the better known algebraic description of the parabola as the graph of a quadratic function in rectangular coordinates. We then introduce the polar coordinate system by imagining what Descartes might have invented if the his ceiling of his bedroom was decorated with a circular design. Hmmm...

How do you compute a derivative whenever your function is expressed in polar coordinates? Let @theMathSinger show you!

This final video in the COVIDeo Calculus II series explores how to calculate area and arc length of functions that are expressed in polar coordinates.

The integral of sec(x) is traditionally derived by using a "trick" that presumes a priori that the solution is already known. This video shows how find the integral of sec(x) by using a very unexpected u-substitution that leads to an integrand that can be evaluated using the method of partial fraction decomoposition.

Students often believe that there is a particular technique that must be used to evaluate a given integral. Nothing could be further from the truth! In this video, a single integral is evaluated in 4 different ways by using 3 basic integration techniques. Watch them all, and be prepared to wow your teacher with your new integration skills!

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