Скачать или смотреть Diff Eqs Lect #15, Real-Life Meaning of Solutions, Van der Pol Eq, SIR Model, Lorenz Attractor

Differential Equations (with DE Tools Printed Access Card) 4th Edition, by Blanchard, Devaney, and Hall: https://amzn.to/3a6E3J2
Differential Equations Lectures Playlist:    • Differential Equations Course, Lecture #1,...  
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Lecture 15. (0:00) Overview of (very full) class period. (2:50) Guidance on a linearity proof (#8a from Section 2.3 from 4th edition of Blanchard, Devaney, Hall). (8:37) Real-life interpretations of solutions to interacting species models and damped harmonic oscillator models (Locator used in Mathematica along with Manipulate and NDSolve to change locations of initial conditions with the cursor). Separatrices (stable & unstable manifolds) discussed. (30:50) Use Euler's method in the context of the Van der Pol oscillator, and its attracting periodic solution. Discussion of Existence and Uniqueness implications. (40:48) Quick summary of the SIR model of an epidemic, with an emphasis on the interesting prediction that "S" does not approach zero as time increases (not everyone gets sick, which is what we see in real life!). (48:46) Quick summary of the Lorenz system and the picture of the Lorenz attractor as an interesting example of non-trivial and chaotic behavior in a 3-dimensional system.

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