Introduction to Nonlinear Dynamics and Chaos
|Professor Joel Zylberberg||
|326 Lewis|| |
Office hours: Mon and Tues 3-4 pm
I will be on Skype during my office hours for EDGE students and anyone else who can't make it in person
Skype name: joelzy.amath
Office hours: 129 Lewis
Yian: Wed 2:30-3:30 (skype: amath402502ta )
Yue: Thurs 4:00-5:00 pm (skype: amath402502ta )
HW due most Fridays at 4 PM (Schedule, and homework scores, available via UW Canvas)
MT: In class on Wed Feb 11 2015
Final Exam (date TBA). See UW Exam schedule for details
Online discussion forumWe'll use the Piazza system for on-line discussion of questions arising from lectures, or homework, etc. Please post and answer questions there. The TA's and Professor will also answer questions posted there.
into browser ... (yes, it's 40250)
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Textbooks, Notes, and Course Resources
The required text for this course is Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering, by S. Strogatz. Perseus Books, 2001.
Online Video Lectures: Videos of the 2015 (502) lectures will be available here (UWlogin required)
For interest, here is A great recent paper on limit cycles and bifurcations in biological oscillators.
Here is the famous "Period 3 implies chaos" paper by Li and Yorke.
John Guckenheimer's famous work on geometric Lorenz attractor "Structural stability of lorenz attractors"
Yian Ma's work, which further simplified the attractor to be the Baker map on the Ponicare section "Potential Function in a Continuous Dissipative Chaotic System: Decomposition Scheme and Role of Strange Attractor"
OTHER COURSE RESOURCES:
Video by S. Strogatz -- Nonlinear dynamics and chaos: Lab demonstrations
JAVA and MATLAB software for odes -- pplane and dfield
EDGE STUDENTS PLEASE UPLOAD YOUR WORK TO CANVAS
(1) One-dimensional systems
First-order ordinary differential equations and initial-value problems
Nonlinear differential equations and flows on the line
Flows on the circle
(2) Two (and higher)-dimensional flows
Linear equations with constant coefficients: matrices and eigenvalues
The phase plane
Bifurcations in two dimensional systems
(3) Discrete-time systems
Introduction to maps
The Lorenz equations
Additional topics in fractals and chaos
MOVIE: synchronized fireflies!
EXAMS AND GRADING:
Midterm in class
!!!! BRING A BLANK EXAM BOOK TO THE MIDTERM !!!!
*** Edge students: contact EDGE office for exam arrangements -- as per their instructions, exams are done remotely in most cases. ***
Students in virtual sections: will take exam in class at same time as other on-campus students.
!!!! BRING 2 BLANK EXAM BOOKS TO THE FINAL !!!!
Homework due most Fridays.Late HW is not accepted, but the lowest HW score will be dropped. This policy is meant to assist in unexpected situations. In unusual extenuating circumstances involving more than one week, please contact the professor.
Homework is graded statistically.
Your course grade will be calculated via the following weights:
homework 30%, midterm 30%, final exam 40%
U Washington takes academic honesty very seriously! You are expected to uphold the strong academic tradition here at UW.