Math 493H/593G Fall 2014

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Course Information[edit]

Description: Applied Dynamics/Chaos.

Instructor: Casian Pantea. email me

Class schedule: Tuesdays, Thursdays, 10:00-11:15AM in Armstrong 313

Office hours: Tuesdays 2-3PM, Thursdays 5-6PM, and by appointment, in Armstrong Hall 305B

Info sheet containing more or less the stuff on this webpage.

Textbooks and resources[edit]

Textbook:

Strogatz, Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering

Useful free resources:

Linear algebra notes

Linear Algebra Done Wrong, Treil
Linear Algebra -- wiki textbook

Web goodies

Strogatz's course at Cornell
Wikipedia
Khan Academy


Evaluation[edit]

Grading scheme[edit]

  • 30% Final exam on Tuesday December 11 2014, 8AM-10AM in Armstrong 315
  • 25% Midterm exam
  • 45% Homework assignments

Homework[edit]

  • Homework will be assigned once every three weeks, and due two weeks later (please see the course schedule below for exact dates).
  • Late turn-ins will not be accepted.

Midterm[edit]

  • There will be one in-class midterm exams, on October 21.
  • No make-up midterm will be given.

Final Exam[edit]

  • Tuesday December 11 2014, 8AM-10AM in Armstrong 315.
  • Final is cumulative.

Course Schedule (subject to changes)[edit]

Date Topic Resources HW/Exams
Aug 19 Introduction Chapter 1
Aug 21 Flows on the line Chapter 2
Aug 26 Bifurcations 3.1-3.4
Aug 28 Overdamped bead on a rotating hoop 3.5
Sep 2 Catastrophes; insect outbreak 3.6-3.7
Sep 4 Flows on the circle 4.1-4.2 HW 1 posted
Sep 9 Firefly synchronization. Two dimensional systems 4.5; 6.1
Sep 11 Linear systems 5.2
Sep 16 Linear systems 5.2
Sep 18 Fixed points and linearization 6.3
Sep 23 Predator-prey models 6.4
Sep 25 Conservative systems 6.5
Sep 30 Lotka-Volterra
Oct 2 Pendulum 6.7
Oct 7 Index theory; limit cycles 6.8, 7.1 HW 2 posted
Oct 9 More on periodic orbits. Poincare-Bendixson Theorem 7.2-7.3
Oct 16 Review
Oct 21 Midterm Midterm solutions
Oct 23 Review
Oct 28 Examples of oscillatory behavior 7.3, 7.5
Oct 30 Liapunov functions
Nov 6 Oscillating chemical reactions HW 2 due
Nov 11 Bifurcations in 2D 8.1
Nov 13 Hopf bifurcations 8.2
Nov 18 Research project: chemical dynamics in 2D
Nov 20 The Lorenz system 9.2 HW 3 posted
Dec 2 Chaos; Strange attractor 9.3
Dec 4 Fractals 11
Dec 9 Math modeling: bird flocks
Dec 11 Final exam

Inclusivity statement[edit]

The West Virginia University community is committed to creating and fostering a positive learning and working environment based on open communication, mutual respect, and inclusion. If you are a person with a disability and anticipate needing any type of accommodation in order to participate in this class, please advise me and make appropriate arrangements with the Office of Accessibility Services (293-6700). For more information on West Virginia University's Diversity, Equity, and Inclusion initiatives, please see http://diversity.wvu.edu.