CALCULUS I

This video introduces the concept of infinite series and discusses what make them converge. The formula to determine the sum of an infinite Geometric Series is derived, and The nth Term Test to check for convergence is explained. & examples are then worked out.

This video introduces Infinite Sequences, gives examples of how to find limits of these sequences, and shows a couple of important theorems thatb are helpful.

This model develops the Logistical Growth Model from the differential equation which incorporates the idea of exponential growth up to a certain point, but where limitations in real life prevent this growth from continuing after a certain point. Two examples are given although the last part of the second one is left for the student to finish as I didn't want the detail involved to dampen the enthusiasm over seeing what this model can accomplish.

This video derives Euler's Method to approximate the solution to a Differential Equation and gives 4 examples of its use. An attempt is made to show how the approximations compare to the actual solutions.

In this video, an explanation is given as to what makes an integral improper and then how to solve improper integrals. In this discussion, Gabrielle's Horn is studied giving students anj incentive to check out "the Painter's Paradox". 4 area examples are then worked out which involve taking improper integrals.

In this video, 4 examples are given doing integration of rational functions. One was done by dividing one polynomial into the other. The others used Partial Fraction Decomposition. Even though B/C Calculus in high school only requires non-repeated linear factors, I did one with repeated linear factors and one with an irreducible quadratic factor. I think it's important that students should see these before going to college.

This video explains the technique of evaluating integrals called Trigonometric Substitutions and gives 5 examples.

In this video, 7 examples are given describing the thought process when attempting to solve integrals where Trigonometric Functions are involved. This is not a Calculus B/C topic, but several important A/B and B/C ideas come into play in solving these integrals. Also the importance of Trigonometric Identities is seen.

This video derives the formula for Integration by Parts and gives 7 examples.