MAE5790-1 Course introduction and overview
Why Mathematics Stack Exchange recommends it
Mathematics Stack Exchange answerers point people to it as the companion lecture series to Strogatz's 'Nonlinear Dynamics and Chaos' for self-study, and one asker cites it as their source for a phase-line argument.
Recommended by 2 people across 3 different months, 2016 to 2018.
What it is
The first lecture of Steven Strogatz's Cornell course on nonlinear dynamics (MAE5790). It gives a historical and logical overview, then starts on one-dimensional systems, fixed points, stability and the logistic equation, following Chapter 1 and Sections 2.0 to 2.3 of his textbook.
What people said
Strong rec Steve Heim · 2016-05 · Mathematics Stack Exchange · on “Mathematics for Guidance, navigation and control”
Here are some of the books I've enjoyed. Note that I'm from an engineering background, and I do robotics and specialise in optimal-control and systems with non-linear dynamics. Nonlinear Dynamics and Chaos [LINK] , Strogatz. This is very approachable and he actually also has lectures [this video] online if you prefer that format. It's not specific to the applications you have in mind, but it does cover a very important part (nonlinear dynamics), which is where a lot of research is pushing at the moment. Dynamic Programming & Optimal Control [LINK] , Berstekas. From my point of view, this text is quite rigorous. Very thorough if you want to get into optimal-control, and stuff like trajectory-optim
Recommends Steve Heim · 2017-04 · Mathematics Stack Exchange · on “How feasible is it for a high school student to explore nonlinear dynamical systems/chaos theory in a research paper?”
I highly recommend Steven Strogatzs' book "Nonlinear Dynamics and Chaos". He also has course lectures online [this video] which follow the book.
Recommends BAYMAX · 2018-05 · Mathematics Stack Exchange · on “Nonlinear dynamics book for self study”
Above are nice texts but I would also like to add a few texts and links which may help - For motivation and literature of how Chaos theory came into existence - refer [LINK] The text by Steven Strogatz is also nice!, better to also see his lectures on Youtube if you want for the basics :) here [this video] . Also this question has some similarity as in the project you will definitely want to mention graphs and curves - Computational text recommendation for non-linear dynamics/differential equations? (flows, maps, nonlinear time-series analysis) [LINK] and Reference request: Nonlinear dynamics graduate reference [LINK] may help too!. Finally, there is a chat room created by me dedicated to Dynamic
Cites qwert4321 · 2016-10 · Mathematics Stack Exchange · on “In the IVP, $x'=\sin(x)$ , x(0)=$\pi$/4 , why must x(t) never equal $\pi$?”
Consider the IVP: $x'=\sin(x)$ , x(0)=$\pi$/4 I want to understand why x(t) can never equal $\pi$. Now I understand that this ODE can be solved analytically. But in the resource I am using, i.e. the linked part of the lecture: [this video] Professor Strogatz manages to show that the asymptotic limit is $\pi$ merely by considering the phase plane. Now I understand that if x(t) is never equal to $\pi$, then since $\sin(x)$ is positive on [$\pi$/4,$\pi$), and since $\sin(\pi)$=0, then the limit at infinity must be $\pi$. But why can we deduce (without consulting the analytic solution), that x(t) never assumes the value $\pi$?