Audio Math
A podcast that talks through math problems without using visuals, making it a unique challenge to explain mathematical concepts purely through audio.
Episodes
2nd Order Derivative Problem and Linearity
Will solve and play around with a second order derivative problem that includes word problem intuition using population growth. Think acceleration! Includes linearity practice and analysis.
Linearity And Linear Operators
Will discuss the powerful concept of linearity and introduce linear operators! After introduction to concepts, will use linearity to solve an equation for rabbit population growth in the much discussed rabbit and fox pop growth problem.
Linear Algebra 5 - Raising E To A Matrix
Will discuss raising Euler's number E to a matrix, very cool stuff! Plus will do a follow-up on dominant eigenvector behavior.
Linear Algebra Part 4
Will discuss matrix to matrix multiplication, dot product operation and inverse matrices, enjoy!
Linear Algebra Part 3 - Eigenvectors and Eigenvalues
55 min episode that dives into very fun topic of eigenvectors and eigenvalues. There are quite a few word problems that will be solved and discussed!
Linear Algebra Part 2 - Linear Transformations And More
Will discuss main topic of linear transformations then follow it up with determinants and linear systems of equations, enjoy!
Linear Alebgra - Part 1 - Vectors and Linear Combinations
Will begin discussion of the massive linear algebra math subject! First up, what are vectors and linear combinations??
The Idea Behind This Podcast
Will discuss the idea behind this podcast, which is to relearn math in a completely new way that emphasizes mental math and doing math away from the desk! It is part science project and part accessibility project!
User Guide and Pre-Calculus
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.
E-Based Exp Growth - Short And Sweet
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.
Rocket Science Problem
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!
Change of Variable Intro
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.
Calculus Intro Part 2 - The Integration Process
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!
Calculus Intro Part 1 - The Derivative Function
This episode dives into calculus! In this part 1, we discuss the main ideas behind calculus and then focus on the derivative function.
The Natural Log Derivative - The Reciprocal 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.
Logarithms and Exponential Growth - Part 2
Going to get into the change of base rule for logarithms and really understand it!
Logarithms and Exponential Growth - Part 1
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!
Consistent Doubling Inside Triple Growth
Say there is a blob that is tripling in mass every month, expressed as 3^t. Is there consistent doubling with this phenomenon??
Exponential Growth and Decay
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).
Spring Series Part 3: Simulating scenarios
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).
Spring Series Part 2: The Differential Equation
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.
Spring Series Part 1: Complex Rotation
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.
Euler's Number Raised To a Power
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
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