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'''E-mail:''' daniel.goldman@physics.gatech.edu <br /> | '''E-mail:''' daniel.goldman@physics.gatech.edu <br /> | ||
''' | '''TA:''' | ||
Ellen Liu <br /> | |||
'''Office:''' | '''Office:''' Howey (office hours TBD) <br /> | ||
'''E-mail:''' | '''E-mail:''' eliu82@gatech.edu <br /> | ||
==Course Description== | |||
The course offers an introductory treatment of nonlinear dynamics and chaos, including first order ODE and their bifurcations, phase plane analysis, limit cycles, Lorenz equations, chaos, iterated maps, period doubling, fractals and strange attractors. Teams of students will also conduct one week of self-guided experiments in Prof. Goldman's laboratory and prepare final report/presentation of the results. | |||
==Time and Place== | |||
Tuesday, Thursday, 2-3:15PM | |||
Class: Howey L5 | |||
Lab: W203 | |||
==Homework and Grading== | |||
Homework assignments will be posted on the web every Monday and will be due next Monday. You can discuss problems with each other, but the solutions have to be executed and submitted individually. In general you are expected to comply with the academic honor code. There will also be one midterm exam and a final. The overall grade for the course will be based on the homeworks (~10%), mid-term exam (~20%), final exam (~20%) and a final project (~50%). | |||
==Books== | |||
"Nonlinear Dyanamics & Chaos", Steven H. Strogatz (Westview Press, 2001) | |||
"Pattern Formation and Dynamics in Nonequilibrium Systems", Cross & Greenside | |||
==Course Topics== | |||
Geometrical analysis of ODEs and bifurcations | |||
Maps | |||
Fractals | |||
Pattern formation | |||
Hands-on experiment/simulation/theory via virtual "microlabs" | |||
==Important dates== | |||
Midterm exam (take home): March 13, due March 17 | |||
Final project talks: April 19,24 | |||
Final exam due (report and problems): May 2 | |||
==Course Outline & Schedule== | |||
Jan 9: Lecture 1, intro to the subject | |||
Jan 11: Lecture 2, intro to 1D systems, geometric methods to solve ODEs (Chap 2) | |||
Jan 18: Lecture 2, continued from before, class project discussion (Chap 2) | |||
Jan 23: Lecture 3, Linear stability analysis, existence and uniqueness, finite time singularities (Chap 2) | |||
Jan 25: Lecture 4, numerical methods for solving ODEs (Chap 2) | |||
Jan 30: Lecture 5, intro to bifurcations, (Chap 3) | |||
Feb 1: Lecture 6, imperfect bifurcations (Chap 3) | |||
Feb 6: Lecture 7, flows on the circle/entrainment (Chap 4) | |||
Feb 8: Lecture 8, 2D systems (linear) (Chap 5) | |||
Feb 13: Lecture 9, Nonlinear 2D systems (Chap 6) | |||
Feb 15: Lecture 10, Conservative nonlinear 2D systems (Chap 6) | |||
Feb 20: Lecture 11, Limit cycles (Chap 7) | |||
Feb 22: Lecture 12, Relaxation and weakly nonlinear oscillators, perturbation theory (Chap 7) | |||
Feb 27: Lecture 13, Bifurcations in 2D (Chap 8) | |||
Mar 1: Lecture 14, Quasiperiodicity, Poincare maps, Floquet theory (Chap 8) | |||
Latest revision as of 10:31, 18 April 2023
Class: Physics 4267/6268, Nonlinear Dynamics & Chaos, Fall 2012
Instructor & TA
Instructor:
Prof. Daniel I. Goldman, School of Physics, Georgia Institute of Technology
Office: Howey C202 (office hours: by email)
Phone: (404) 894-0993
E-mail: daniel.goldman@physics.gatech.edu
TA:
Ellen Liu
Office: Howey (office hours TBD)
E-mail: eliu82@gatech.edu
Course Description
The course offers an introductory treatment of nonlinear dynamics and chaos, including first order ODE and their bifurcations, phase plane analysis, limit cycles, Lorenz equations, chaos, iterated maps, period doubling, fractals and strange attractors. Teams of students will also conduct one week of self-guided experiments in Prof. Goldman's laboratory and prepare final report/presentation of the results.
Time and Place
Tuesday, Thursday, 2-3:15PM
Class: Howey L5 Lab: W203
Homework and Grading
Homework assignments will be posted on the web every Monday and will be due next Monday. You can discuss problems with each other, but the solutions have to be executed and submitted individually. In general you are expected to comply with the academic honor code. There will also be one midterm exam and a final. The overall grade for the course will be based on the homeworks (~10%), mid-term exam (~20%), final exam (~20%) and a final project (~50%).
Books
"Nonlinear Dyanamics & Chaos", Steven H. Strogatz (Westview Press, 2001)
"Pattern Formation and Dynamics in Nonequilibrium Systems", Cross & Greenside
Course Topics
Geometrical analysis of ODEs and bifurcations
Maps
Fractals
Pattern formation
Hands-on experiment/simulation/theory via virtual "microlabs"
Important dates
Midterm exam (take home): March 13, due March 17
Final project talks: April 19,24
Final exam due (report and problems): May 2
Course Outline & Schedule
Jan 9: Lecture 1, intro to the subject
Jan 11: Lecture 2, intro to 1D systems, geometric methods to solve ODEs (Chap 2)
Jan 18: Lecture 2, continued from before, class project discussion (Chap 2)
Jan 23: Lecture 3, Linear stability analysis, existence and uniqueness, finite time singularities (Chap 2)
Jan 25: Lecture 4, numerical methods for solving ODEs (Chap 2)
Jan 30: Lecture 5, intro to bifurcations, (Chap 3)
Feb 1: Lecture 6, imperfect bifurcations (Chap 3)
Feb 6: Lecture 7, flows on the circle/entrainment (Chap 4)
Feb 8: Lecture 8, 2D systems (linear) (Chap 5)
Feb 13: Lecture 9, Nonlinear 2D systems (Chap 6)
Feb 15: Lecture 10, Conservative nonlinear 2D systems (Chap 6)
Feb 20: Lecture 11, Limit cycles (Chap 7)
Feb 22: Lecture 12, Relaxation and weakly nonlinear oscillators, perturbation theory (Chap 7)
Feb 27: Lecture 13, Bifurcations in 2D (Chap 8)
Mar 1: Lecture 14, Quasiperiodicity, Poincare maps, Floquet theory (Chap 8)