Spring 2022
Prof. R. Ganesh
Author: Vishnu Sankar
Pre-requisite skills: MATLAB programming
Course Content:
- First-order Ordinary Differential Equations (ODEs) - Stability and Bifurcations
- Second-order ODEs - Phase plane analysis, Limit Cycles, and Bifurcations
- Asymptotic methods for nonlinear oscillators - free and forced response
- Computational methods and Stability of periodic solutions (Floquet theory)
- Chaos in Dynamical systems
Motivation to take up the course: Nonlinearity is so fundamental that is can be observed in pretty much every field across science and engineering, phenomena like flutter is a classic example in aerospace engineering that is bound to the principles of non-linearity. This course does justice in unraveling the mysteries of such non-linear concepts.
Course Evaluation Structure:
- HW 1,2,3 : 7%, 7%, 6%
- Mid Sem: 25%
- End Sem: 40%
- Term Project: 15%
Quizzes/Midsem/Endsem papers Difficulty: 4/5
Assignments/Project Difficulty: 3/5
Info about Projects/Assignments: The assignments were very lengthy and time consuming, but sadly each assignment carries only 7%. The final project includes a project presentation and a report submission, you are free to choose any topic of your interest. You are expected to implement some of the concepts through numerical implementation. Working on the assignments diligently helps a lot in acing through the project.
General funda: The assignments are lengthy so get started with them as soon as possible. The exams have a few questions similar to the ones in assignments, so solve your assignments diligently. A class of about an hour and a half is very tiresome for this course, try not to loose track of the lectures.
Professor’s Teaching Style: The lectures are detailed and to the point, the professor shows example problems solved numerically in MATLAB.
References OR online resources:
- Non-linear Dynamics and Chaos, book by Prof. Steven Strogatz
- Lecture series by Prof. Steven Strogatz: https://www.youtube.com/playlist?list=PLbN57C5Zdl6j_qJA-pARJnKsmROzPnO9V
- Lecture series by Prof. Shane Ross: https://www.youtube.com/playlist?list=PLUeHTafWecAUqSh3Gy0NNr7H3OsXoC-aK
Should you do this course?: The course presents an intuitive and graphical approach to nonlinear phenomena. The first half of the course is more about equipping oneself with the graphical approaches to find unstable and stable solutions of nonlinear equations. The second half of the course is little more mathematically involved without losing track of the visual approaches involved to tackle such problems. If you are interested in diving deep to learn about the patterns that are present hidden in the so called ‘Chaotic phenomena’ (such as turbulence) this course gives you the right tools to do so.