Audio Math – Details, episodes & analysis

Will give guidance on how to listen to this podcast and what episodes to start on given your math background. Also will do a crash course in pre-calculus math needed for any episode.

Will share my favorite way to understand exponential growth and how this reveals the importance of Euler's number "e". And discuss how e^x and natural log functions are two sides of the same coin.

Going to discuss exponential growth and decay!

Will talk about discrete and continuous cases for both. Will walk through examples and the math that powers them!

Note: Early on I misspoke, I said 112^2, when I meant 100*(1.12^2).

This is a series on modeling the position of a mass on a spring at any time.In this part 3, the discovered "spring mass position" solution will be used to see how the mass will behave given specific initial conditions, including mass size, spring strength and amplitude (how much the spring is pulled back).

This is a series on modeling the position of a mass on a spring at any time.In this part 2, there is the establishment of a differential equation describing the spring mass dynamics, then working toward the "position of the mass" solution.

This is a series on modeling the position of a mass on a spring at any time.

Discussed in this part 1 is complex rotation, which is the base of understanding needed for the rest of the series.

Will discuss Euler's number "e" raised to a power or even an imaginary power. Will be using a really cool definition of exponential growth to further understand e raised to some power. Raising to a power results in exponential growth. Raising to an imaginary power results in complex rotation. And finally "e" raised to the pi times "i" equals -1. Yeah, we'll go there!

Let's do a rocket science problem! Will calculate accumulated velocity of a rocket from takeoff and include the rocket changing mass due to fuel burning. Will use change of variable to solve things. As always, will focus on finding deeper meanings!

Let's see how change of variable or u-substitution can be done to a simple integral problem. Change of variable is a powerful tool for simplifying harder integrals, but this episode will be for intro to change of variable. Will do a follow-up episode using change of variable to simplify a more difficult rocket science problem.

We discuss the integration process in this part 2 of calculus intro, which is about taking a derivative function and using it to compute back the original accumulation function. Enjoy!