Math 350, Spring 2019

 Dynamics and Chaos 

 

Instructor                      John E. McCarthy
Class                              MWF 9.00-10.00, Cupples I Rm 218
Midterm                         Friday March 1st 
Final                               Friday May 3rd, 8.00-10.00 a.m.


Office                          105 Cupples I
Office Hours               M 4.00-5.00, We 10.00-11.00,  Th. 3.00-3.45, and by appointment
Phone                          935-6753

Prerequisites               Math 217 (Differential Equations) and 233 (Multivariable Calculus)

 

Description
One of the great mathematical discoveries of the 20th century is that nearly all naturally occuring systems are chaotic -
small changes in the initial conditions will lead to large changes in the long-term behavior.
This means that predictions can only be made for a characteristic time period.
This can be days for the weather, hundreds of millions of years for planetary motion, or seconds for some chemical reactions.
But there is a theoretical limit to how well predictions can do.

This course shall investigate dynamical systems, with applications to various fields of science, and how chaos arises.

Homework

There will be weekly homework sets during the semester, assigned on Friday and due the following Friday.

 

Content

  1. Flows on the line
  2. Bifurcations
  3. Flows on the circle
  4. Linear Systems
  5. Phase Plane
  6. Limit Cycles
  7. Lorenz equations
  8. Chaos
  9. Fractals
  10. Strange attractors

 

Basis for Grading

Attendance and class participation will be 5% of your grade, homework will be 30%, the midterm will be 30%, and the final will be 40%.

Homework

Homework is an extremely important part of the course. Whilst talking to other people about it is not dis-allowed, too often this degenerates into one person solving the problem, and other people copying them (often justified to themselves by saying "I provide the ideas, X does the details" - but the details are the key. If you can't translate the idea into a real proof, you don't understand the material well enough). So I shall introduce the following rules:
(a) You can only talk to some-one else about a problem if you have made a genuine effort to solve it yourself.
(b) You must write up the solutions on your own. Suspiciously similar write-ups will receive 0 points.

Class

I expect you to come to class every day, and to participate in class discussions.
I also expect you to stay abreast of the material we are covering, and may call on you at any time to answer a question.

Text          Nonlinear dynamics and Chaos, Second Edition, by S.H. Strogatz   (CRC 2015).

Other books Chaos: Making a New Science by James Gleick is one of the best general interest science books ever written,
capturing the excitement of the discoveries and describing the people who made them.


Websites        Here are some videos:    http://www.clausewitz.com/mobile/chaosdemos.htm             
                        Verhulst and the logistic equation:       http://webpages.fc.ul.pt/~mcgomes/aulas/dinpop/Mod13/Verhulst.pdf  

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The University is committed to offering reasonable academic accommodations to students who are victims of sexual assault.  Students are eligible for accommodation regardless of whether they seek criminal or disciplinary action.  Depending on the specific nature of the allegation, such measures may include but are not limited to: implementation of a no-contact order, course/classroom assignment changes, and other academic support services and accommodations.  If you need to request such accommodations, please direct your request to Kim Webb, Director of the Relationship and Sexual Violence Prevention Center, or Jen Durham Austin, Support Services Counselor. Both Kim Webb and Jen Durham Austin are confidential resources; however, requests for accommodations will be shared with the appropriate University administration and faculty.  The University will maintain as confidential any accommodations or protective measures provided to an individual student so long as it does not impair the ability to provide such measures.

If a student comes to me to discuss or disclose an instance of sexual assault, sex discrimination, sexual harassment, dating violence, domestic violence or stalking, or if I otherwise observe or become aware of such an allegation, I will keep the information as private as I can, but as a faculty member of Washington University, I am required to immediately report it to my Department Chair or Dean or directly to Ms. Jessica Kennedy, the University's Title IX Director.  If you would like to speak with directly Ms. Kennedy directly, she can be reached at (314) 935-3118jwkennedy@wustl.edu, or by visiting the Title IX office in Umrath Hall.  Additionally, you can report incidents or complaints to the Office of Student Conduct and Community Standards or by contacting WUPD at (314) 935-5555 or your local law enforcement agency. See: Title IX

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