Best of AllTime Online Course
Introduction to Dynamical Systems and Chaos
Santa Fe Institute via Complexity Explorer

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Overview
In this course you'll gain an introduction to the modern study of dynamical systems, the interdisciplinary field of applied mathematics that studies systems that change over time.
Topics to be covered include: phase space, bifurcations, chaos, the butterfly effect, strange attractors, and pattern formation. The course will focus on some of the realizations from the study of dynamical systems that are of particular relevance to complex systems:
1. Dynamical systems undergo bifurcations, where a small change in a system parameter such as the temperature or the harvest rate in a fishery leads to a large and qualitative change in the system's
behavior.
2. Deterministic dynamical systems can behave randomly. This property, known as sensitive dependence or the butterfly effect, places strong limits on our ability to predict some phenomena.
3. Disordered behavior can be stable. Nonperiodic systems with the butterfly effect can have stable average properties. So the average or statistical properties of a system can be predictable, even if its details are not.
4. Complex behavior can arise from simple rules. Simple dynamical systems do not necessarily lead to simple results. In particular, we will see that simple rules can produce patterns and structures of surprising complexity.
Taught by
David Feldman
Charts
 #3 in Subjects / Mathematics
 #1 in Subjects / Mathematics / Calculus
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Reviews
4.8 rating, based on 117 reviews

Aleta completed this course.
I appreciated the structured approach to the course material and the painstaking development of foundational concepts. Dr. Feldman presents the course in an informal, acrossthedesk manner. Each lecture feels like you are experiencing an individual tutoring... 
Maxime completed this course, spending 2 hours a week on it and found the course difficulty to be very easy.
This course is perfect for beginners who want to get a grasp of the field of chaos with minimal mathematical/numerical material, but yet enough to have a flavor of the underlying world, beyond the bases. Dave Feldman is a great teacher, very dedicated... 
Class completed this course, spending 2 hours a week on it and found the course difficulty to be medium.
This is a fun class which I would highly recommend. Incredibly accessible course which introduced an interesting branch of mathematics.
If you've done a bit of computer science or programming, this class shows a very interesting result from the simple idea of iteration.
The professor is interesting and makes the material intuitive. Regardless of your level of mathematical comfortability, this class is well paced and provides all the tools you need to proceed through it.
Don't miss this class!! 
Anonymous is taking this course right now.
This was the missing link for me. I had read many popular science books about dynamical systems and chaos, and was eager to gain a more nuanced and technical understanding of the field. The only thing holding me back, of course, was a lack of background... 
Navyanth completed this course, spending 27 hours a week on it and found the course difficulty to be medium.
Thanks for making this course available for all. It really changed the way I see the computational world. I had a masters degree in Computational engineering where I learned about the fundamentals of Continuum mechanics and its applications in Structural... 
Sabine completed this course.
A fascinating course, I absolutely loved it! There was a bit of maths involved, but Dave Feldman walked us through it step by step  so slowly that even somebody who has no idea whatsoever of maths should grasp it. Sitting in front of my laptop on the other side of the globe, I felt he deeply cared that you understood everything  as somebody said above, it almost felt like a personal tutorial! As I had already done Melanie Mitchell's course (equally excellent!), I was familiar with much of the territory, but Dave's approach helped me to understand some of the more difficult concepts. I think the two courses complement each other very nicely. Highly recommended!

David completed this course.
This class was just amazing and great. Mr. Feldman knows how to really get you to see the 'big idea' and that's the most import part of any intro class; to get the big picture. Math was light and not terrifying. Deadline is the class day of class. Quizzes were light and the homework was challenging enough if you wanted it to be. I absolutely loved this class. 
Abhijit completed this course.
A great point for a young person, with knowledge about calculus to start if he or she wishes to pursue this field. This course starts step by step, and is excellent in making the learning about nonlineardynamics an almost effortless process. The homework at the end of each unit are a must do to enjoy the course. Knowing computer programing is really a necessity I would say so. 
Anonymous completed this course.
I completed this course a few years ago just to learn about chaos theory. I loved it! I am a math teacher and this year have an honors precalculus course. I am letting my students complete it for extra credit and the ones doing it are enjoying it so much next year I will require it  perhaps work on it as a class each Friday. Thank you so much for a great course! 
Gaetano completed this course, spending 5 hours a week on it and found the course difficulty to be medium.
I had a great time having this course and Prof. Feldman was so dedicated in diving us into this amazing subject. I think that the course gave us a solid platform in order to go deeper in the study of Dynamical Systems and Complexity. 
Narasimhan completed this course.
Complexity and Dynamical Systems is a fascinating field of mathematics. There are linear, predictable and wellordered systems, like simple physical motion. There are nonlinear systems, like the weather. What are the latter like? Can they be studied... 
Anonymous completed this course.
I enjoyed the course very much. The teacher is great, he can explain both familiar and new (complicated) matter in a fresh and understandable way. I helped me to understand dynamical systems deeper, as I do dynamical modeling in economics. 
Anonymous is taking this course right now.
The effort put into the course becomes clear as soon as you start. A very accessible design of the material without loosing the required depth for a proper understanding of the essence. 
Anonymous completed this course.
Compliments! Well structured course. Interesting and motivating.
Take this course, read Gleicks Book and watch Strogatz lecture and you got your own personal route to chaos.... 
Anonymous completed this course.
Spectacular course. Highlevel teacher. Can you teach a complex issue for people with little mathematical background. I recommend !! Congratulations to the teacher !! 
Davide completed this course.
This course is a awesome mine of information and knowledge on dynamical systems and chaos. It starts at the very beginning by explaining the mathematical bricks necessary to understand the following units, but it's not a heavy mathematical course. Quite... 
Linda completed this course.
I am retired; I've done no mathematics of any significance since the early 70's. This course brought me hours of challenge and joy. Every time I completed homework or unit exams I felt enormous satisfaction. My deepest thanks to Professor Feldman.... 
Nicholas completed this course.
Firstly, the platform is easy to use. It makes focus and moving around content much easier to achieve. Next, the course itself is riveting not just because of the digestibility of the content, courtesy of the instructor, but also the availability of... 
Mariano completed this course, spending 1 hours a week on it and found the course difficulty to be medium.
Leonardo da Vinci said : "Simplicity is the ultimate sophistication" and professor Feldman with his way of thinking exactly represents Leonardo's thougth.
Only great professors uses scissors, pencils and papers and explain very complicated things with ease .
This course is a very good one, professor Feldman's explanations are really clears and complex materials "flows" very well .
Personally have already recommended this course to others and think that I will gladly follow other courses in which professor Feldman will be the teacher considering his high scientific level and his predisposition to teach in a simple way ( where he can ) ...
Simply great !!! 
Anonymous completed this course.
This is a very good introduction to (nonlinear) dynamical systems. Instruction is very good and the provided simulations are very helpful.
I am a math dummy and my background is mostly biology. This class did a so good job in explaining dynamical systems that I realized biological systems are likely to be ( maybe complex) dynamical systems. However, due to experimental limitations, molecular and cellular biologists hardly can study their systems as a dynamical system. After taking this class, I am decided to try to study biological systems (nervous systems, more specifically) as dynamical systems for my future work.