Audio Math

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!

This episode dives into calculus! In this part 1, we discuss the main ideas behind calculus and then focus on the derivative function.

Let's deeply investigate the natural log function and its derivative function, which is the reciprocal function 1/x. Very cool findings in regards to logarithm consistent shift trait and reciprocal function scale invariance trait. Also will discuss logs of any base and their derivative, which is just a reciprocal function transformation.

Going to get into the change of base rule for logarithms and really understand it!

Really great episode on logarithms, their rules and continuous exponential growth. There are easy problems to start and get warmed up, followed by tougher problems to increase understanding. Enjoy!

Say there is a blob that is tripling in mass every month, expressed as 3^t. Is there consistent doubling with this phenomenon??

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).