Channel Title: Prof Ghrist Math Channel Description: this is a channel for those on the road to Mathematics. i'm professor ghrist; you can call me prof-g. i'll be your guide, with finely-crafted video-texts. the premiere products are Calculus BLUE, a video-text for multivariable calculus; and Calculus GREEN, for single-variable calculus (in progress). a physical book -- Calculus Blue Guide -- is a 200 page guide full of discussion questions, exercises, answers, and more: available on Amazon at: https://www.amazon.com/Calculus-Blue-Guide-Robert-Ghrist/dp/1944655077/ there are video-matching electronic-texts for calc BLUE with exercises, custom designed for phones & laptops, are at the amazon kindle store: https://www.amazon.com/Calculus-BLUE-Multivariable-Vectors-Matrices-ebook/dp/B019IY9G7Q additional resources for teachers & students can be found at https://www2.math.upenn.edu/~ghrist/BLUE.html original soundtrack by EPLIAX streaming on Amazon/Apple/Spotify/etc... see the video at https://www.youtube.com/watch?v=ekq3jmU0wcc <video> CalcGREEN 2 : Ch. 6.2 : Types of Equilibria Description: Equilibrium solutions to differential equations are all important, but they're not all alike. Let's take a look at how to distinguish equilibria based on stability. </video> <video> CalcGREEN 2 : Ch. 5 : THE BIG PICTURE Description: </video> <video> CalcGREEN 2 : Ch 6.3 : Visualizing ODEs Description: We have been plotting solutions to the ODE dx/dt=f(x) as x(t) depending on t. What happens if we change the way we visualize solutions? A lot more structure appears, especially with respect to equilibria. </video> <video> CalcGREEN 2 : Ch. 5.1 : Taylor Time Description: Let's think back to what we have done previous with Taylor expansion and begin the process of applying these ideas to terms in a differential equation. </video> <video> CalcGREEN 2 : Ch. 6.4 : The Stability Criterion for Equilibria Description: There's a great method for classifying the equilibria in a first-order ODE of the form dx/dt = f(x). What's the magic ingredient? Taylor expansion! </video> <video> CalcGREEN 2 : Ch. 4.2 : Integrating Factors Description: Here's a method that works for nonautonomous affine ODEs -- the method of integrating factors. </video> <video> CalcGREEN 2 : Ch. 5 : Series & ODEs Description: Hey, what happened to Taylor expansion? Oh, that's still relevant and useful. Let's see what Taylor series can say about differential equations. </video> <video> CalcGREEN 2 : Ch. 6.1 : Nonlinear ODEs, oh no Description: Oh no! Nonlinear ODEs are the most useful types, and they are usually impossible to solve. So, let's stop searching for exact solutions are try thinking more qualitatively. </video> <video> CalcGREEN 2 : Ch. 5.4 : Nonlinear ODEs & Series Description: Series expansion has worked well for linear ODEs, but what happens when we move into the world of (simple) nonlinear ODEs? </video> <video> CalcGREEN 2 : Ch. 5.3 : Simple Harmonic Example Description: Let's see how series solutions to ODEs work in the case of a 2nd-order ODE: a simple harmonic oscillator. </video> <video> CalcGREEN 2 : Ch. 4 : THE BIG PICTURE Description: </video> <video> CalcGREEN 2 : Ch. 5.2 : Exponential Example Description: Let's see how series solutions to ODEs work in the simplest setting -- the linear 1st-order ODE. </video> <video> CalcGREEN 2 : Ch. 4.4 : So Many ODEs Description: After digging into two more examples of nonautonomous affine ODEs and their integrating factors, we will... give up -- since there are so many classes of difficult ODEs out there! We'll try learning a few more methods, but keep in mind that you need a lot of time and effort (and a dedicated course) to get good at general differential equations. </video> <video> CalcGREEN 2 : Ch. 4.3 : Stirred Tank Redux Description: Let's go back to the example of a stirred mixture in a tank and see what the method of integrating factors can do to assist. </video> <video> CalcGREEN 2 : Ch. 6 : Equilibria & Linearization Description: Nonlinear ODEs are just. Too. Hard! So let's take some time and learn a few qualitative tools for differential equations. Along the way, we will see just how what we learned in Volume 1 impacts the behavior of solutions. </video>

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Description

this is a channel for those on the road to Mathematics.
i'm professor ghrist; you can call me prof-g. i'll be your guide, with finely-crafted video-texts.

the premiere products are Calculus BLUE, a video-text for multivariable calculus; and Calculus GREEN, for single-variable calculus (in progress).

a physical book -- Calculus Blue Guide -- is a 200 page guide full of discussion questions, exercises, answers, and more: available on Amazon at: https://www.amazon.com/Calculus-Blue-Guide-Robert-Ghrist/dp/1944655077/

there are video-matching electronic-texts for calc BLUE with exercises, custom designed for phones & laptops, are at the amazon kindle store:
https://www.amazon.com/Calculus-BLUE-Multivariable-Vectors-Matrices-ebook/dp/B019IY9G7Q

additional resources for teachers & students can be found at https://www2.math.upenn.edu/~ghrist/BLUE.html

original soundtrack by EPLIAX streaming on Amazon/Apple/Spotify/etc...
see the video at https://www.youtube.com/watch?v=ekq3jmU0wcc

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