product rule Archives - Infinity is Really Big

January 27, 2020January 29, 2020

Integration by Parts (and Linear Motion)

Calculus 2, Lectures 3B through 4 (Videotaped Fall 2016)

*Integration by parts is needed to compute the definite integral to find the area under this curve representing the speed of a linear motion.*

You might say that integration by parts is an “unexpected” or “surprising” method of integration.

While the other main method, integration by substitution, can be thought … Read the rest

November 30, 2019November 30, 2019

Infinitesimal Calculus and Calculus Rules

Calculus 1, Lectures 16A through 18A

Infinitesimal calculus can be used to derive the derivative of the sine function.

Did you know that Newton and Leibniz did not know the precise definition of a limit?

Instead, they approached calculus in an intuitive way. Today, this intuitive method is called infinitesimal calculus. It is based on the concept of … Read the rest

February 1, 2019February 1, 2019

New Video: Immunization, Part 2

In the previous post, “New Video: Immunization, Part 1“, I introduced the idea of Redington immunization of liability cashflows by asset cashflows.

It was a post that delved into the details of my previous YouTube video “Actuarial Exam 2/FM Prep: Use Redington Immunization to Find a Ratio of Assets in a Portfolio” embedded … Read the rest