Nonlinear Dynamics and Chaos - May 2019
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Syllabus
Course Syllabus - 2019
Socrative App Classroom: BIERI2879 -
Daily Information, Homework Assignments, and Reading
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Monday May 6th - DAY 1 - CLICK HERE - Week 1 Homework Assigned
*** Homework ***
Read Nonlinear Dynamics and Chaos (Strogatz) Introduction Pages 1-11. You should already have a copy of the BOOK!
WEEK 1 Homework Problems - Due Monday May 13th by 8:59am Homework 1
*** In Class Materials ***
Logistic Example
Interesting Videos - Click Here
Group Work - Day 1
*** Extra Help and Review Materials ***
Integration Practice
Integration Practice Solutions
Algebra Cheat Sheet
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Tuesday May 7th - DAY 2 - CLICK HERE
*** Homework ***
Read Nonlinear Dynamics and Chaos (Strogatz) Chapter 2 Pages 15-24. By now you should have a copy of the book.
WEEK 1 Homework Problems - Due Monday May 13th Before Class - We have covered through Population Dynamics
*** In Class Materials ***
Group Work - Day 2
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Wednesday May 8th - DAY 3 - CLICK HERE
*** Homework ***
Read Nonlinear Dynamics and Chaos (Strogatz) Chapter 2 Pages 24-31.
WEEK 1 Homework Problems - Due Monday May 13th Before Class - We have covered through Existence and Uniqueness
*** In Class Materials ***
Group Work - Day 3
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Thursday May 9th - DAY 4 - CLICK HERE
*** Homework ***
Read Nonlinear Dynamics and Chaos (Strogatz) Chapter 2 Pages 31-36.
WEEK 1 Homework Problems - Due Monday May 13th Before Class - You should be able to handle all of the problems
Study session today at 2:30pm!!
*** In Class Materials ***
Euler Method
Improved Euler Method
Runge Kutta Method
Group Work - Day 4
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Monday May 13th - DAY 5 - CLICK HERE - Week 2 Homework Assigned
TOMORROW CLASS WILL BEING AT 1pm
*** Homework ***
Read Nonlinear Dynamics and Chaos (Strogatz) Chapter 3 Pages 45-51. Make sure you are reading along with the class and doing well on the quiz at the beginning of class each day!
Homework Week 2 - Due Monday May 20th BEFORE CLASS
*** In Class Materials ***
Group Work Activity
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Tuesday May 14th - DAY 6 - CLICK HERE
*** Homework ***
Read Nonlinear Dynamics and Chaos (Strogatz) Chapter 3 Pages 51-62. Make sure you are reading along with the class and doing well on the quiz at the beginning of class each day!
Continue working on Homework Week 2.
*** In Class Materials ***
Group Work Activity - Dr. Jagu
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Wednesday May 15th - DAY 7 - CLICK HERE
*** Homework ***
Read Nonlinear Dynamics and Chaos (Strogatz) Chapter 3 Pages 62-70 (really try to understand the bead on a tilted wire example since we won't officially do this in class but it is interesting). Make sure you are reading along with the class and doing well on the quiz at the beginning of class each day!
Continue working on Homework Week 2.
*** In Class Materials ***
Group Work Activity - Full Analysis
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Thursday May 16th - DAY 8 - CLICK HERE
*** Homework ***
Read Nonlinear Dynamics and Chaos (Strogatz) Chapter 3 Pages 70-80. Make sure you are reading along with the class and doing well on the quiz at the beginning of class each day!
Continue working on Homework Week 2 - Due Monday 5/20 before class!
*** In Class Materials ***
Group Work Activity - Brain Slug Outbreak
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Monday May 20th - DAY 9 - CLICK HERE - Week 3 Homework Assigned
*** Homework ***
Read Nonlinear Dynamics and Chaos (Strogatz) Chapter 5 Pages 125-131.
Homework Week 3 - Due Monday May 27th before class begins
*** In Class Materials ***
Group Work Activity
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Tuesday May 21st - DAY 10 - CLICK HERE
*** Homework ***
Read Nonlinear Dynamics and Chaos (Strogatz) Chapter 5 Pages 131-141.
Continue working on Homework Week 3
*** In Class Materials ***
Eivenvalue Code
Group Work Activity
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Wednesday May 22nd - DAY 11 - CLICK HERE
*** Homework ***
Read Nonlinear Dynamics and Chaos (Strogatz) Chapter 6 Pages 146-153.
Continue working on Homework Week 3
Go over and redo problems that you missed on the last homework. Make sure you understand these bifurcation problems!
*** In Class Materials ***
Problem 4 worked in class
Bifurcation Diagram Problem 4
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Thursday May 23rd - DAY 12 - CLICK HERE
*** Homework ***
Read Nonlinear Dynamics and Chaos (Strogatz) Chapter 6 Pages 154-160.
Continue working on Homework Week 3 - Due Monday before class.
*** In Class Materials ***
Group Work Activity
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Monday May 27th - DAY 13 - CLICK HERE - Week 4 Homework Assigned
*** Homework ***
Read Nonlinear Dynamics and Chaos (Strogatz) Chapter 7 Pages 198-202 and Chapter 8 244-251.
Review all material from the course. Look over lecture notes and re-read sections in the book that still confuse you. Please come to class on Wednesday with questions if you have them!
Homework Week 4 - Due Thursday May 30 along with the final exam. Solutions will be posted on Wednesday.
*** In Class Materials ***
REVIEW SESSION:
Group Work Activity
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Tuesday May 28th - DAY 14 - CLICK HERE
*** Homework ***
Review all material from the course. Look over lecture notes and re-read sections in the book that still confuse you. Please come to class on Wednesday with questions if you have them. Try to take time to relax and draw a fractal!
Don't forget to sign up to present problems in class for Extra Credit!
*** In Class Materials ***
Strange Attractor Trajectories
Mandelbrot Zoom
Nova Series - Hunting the Hidden Dimension
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Wednesday May 29th - DAY 15 - CLICK HERE - HAND OUT FINAL EXAM
*** Homework ***
FINAL EXAM HANDED OUT IN CLASS TODAY! - Final exam handed in to Joanna (or under her office door) by 6pm Thursday May 30th.
*** In Class Materials ***
In Class Presentations
Each day I will post reading assignments and additional information. If we have in class projects they will be posted here.
Each Monday I will assign new homework which should be completed daily and handed in on the following Monday BEFORE CLASS. You can drop scanned or typed assignments or numerical code into our class Google folder: Email Joanna for the Link. Please put your work in your folder and clearly name the items.
Click on the links below to see the information for that day. -
Monday May 6th - DAY 1 - CLICK HERE - Week 1 Homework Assigned
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Homework Solutions, Videos, and Extra Practice Problems
** HOMEWORK SOLUTIONS **
WEEK 1 Solutions
Euler
Improved Euler
Runge Kutta
WEEK 2 Solutions
WEEK 3 Solutions
WEEK 4 Solutions
** VIDEOS **
1. A great physics video about Magnetic Hysteresis. Can you interpret what he is saying in terms of a Bifurcation Diagram Sketch?
2. When two or more chaotic systems are coupled they can exhibit synchronization. Fireflies blinking in unison or inanimate objects spontaneously synchronizing their movements.
A Ted talk by the author of our textbook Steven Strogatz:
3. Benoit Mandelbrot - developed the idea of fractals and roughness in mathematics. Here is a wonderful Ted talk by this amazing mathematician given less than a year before he died at the age of 85.
4. The Briggs-Rauscher reaction. An example of an oscillating chemical reaction.
If you find great vieos about nonlinear dynamics or chaos, send them to Joanna and she will post theme here to share with the class!! -
Lecture Notes, Software, and Additional Info
Here is a list of software and links to usefull websites for this class
Dfield - download
Pplane - download
Website for Dfield and Pplane
Desmos Graphing Calculator - General Graphing with Parameter Slider
Desmos Calculator - Direction Field
LECTURE NOTES:
USE AT YOUR OWN RISK - There could be (and most likely are!) typos that are corrected in class, so please use common sense and your own notes to compare to what you see here:
Day 1 - What is Dynamics - Reduction of Order - Classification of Equations
Day 2 - Flow on a Line - Fixed Points and Stability - Phase Portraits
Day 3 - Linear Stability Analysis - Existence and Uniqueness
Day 4 - Potentials - Numerical Methods for Nonlinear Equations
Day 5 - Introduction to Bifurcations - Saddle Node Bifurcations
Day 6 - Transcritical and Pitchfork Bifurcations - Using Taylor Series to Analyze Bifurcations
Day 7 - More Complicated Examples - Class time to practice homework problems
Day 8 - Imperfect Bifurcations and Catastrophes
Day 9 - Two Dimensional Systems - Phase Planes
Day 10 - Two Dimensional Systems - Eigenvalues and Eigenvectors
Day 11 - Nonlinear Two Dimensional Systems - Jacobian
Day 12 - More practice with Two Dimensional Nonlinear Systems
Day 13 - Bifurcations in 2-D Systems - Limit Cycles
Day 14 - Hopf Bifurcations, Lorenz Equations, Chaos and Fractals.
Day 15 - Planned Review Day - Final Exams Handed Out
I sense a bifurcation about to happen!
Photo thanks to cuteoverload.com