CALCULUS I

In this last video (for a Calculus I and II course in college or Calculus A/B and B/C in high school), 2 more Polar problems are worked out along with one more comprehensive problem (involving ice cream).

This video has 3 Polar Problems. In them, some aspects of earlier topics are interwoven with Polar ideas. Also discussions of what such derivatives as dr/d(theta) and dy/d(theta) signify in a problem. Some of these problems require a graphing calculator although they can be understood without one.

This video derives formulas to calculate slopes and arc lengths when using Polar Equations. It shows 2 examples of each as well as doing one more polar area problem.

This video quickly introduces Polar Co-ordinates and relationships. A derivation is given for the formula to find area in Polar. 5 examples are then given.

This video is the last on Parametric Equations. A quick introduction is made to the importance of parametric representations when you get to vector Calculus. A short summary is given at the end of the video of the important topics in encountered when using Parametric Equations). (Answer at very end of video should be Pi Sqrt(10) , not SQRT(10Pi) ) - Captain Derivative must have been getting tired!

This video gives 5 examples of finding various things of interest when a relationship is given Parametrically (graphing, slopes, concavity, arc lengths, volumes of revolution, surface area).

This video introduces Parametric Equations. It also derives formulas to find direction of movement, slope, arc length, speed of movement, and concavity. 3 examples are given.

This video attempts to give a good final example of how to find the Taylor Series of a function along with the use of a related Taylor Polynomial to estimate a function value for a given x (and looking at the associated error prediction). An example is also given to show the use of Taylor Series to solve Differential Equations which may show up in an advanced Physics course. Lastly, just because everyone should see it, I gave a proof of Euler's Formula to show the beauty that Always exists in our Universe even when things aren't looking that good. Sorry, but I ended with an out of tune song that "sums" up the chapter on Taylor Series!

This video attempts to explain the significance of the "center" and the # of terms kept when a Taylor Polynomial is used to approximate a function. Several examples are given.