MA 573 Qualitative Theory of Ordinary Differential Equations

MA 573 - Qualitative Theory of Ordinary Differential Equations

Course Information

Lecturer: Ryan Goh
Lectures: Monday,Wednesday,Friday, 10:10am-11:00 am; CAS 243
Office Hours : Wednesday 11:00am - 12pm, Thursday 11am-12pm or by appointment.
Syllabus: HTML here
Textbook: "Differential Equations, Dynamical Systems, and an Introduction to Chaos" by Morris W. Hirsch, Stephen Smale, Robert L. Devaney; 3rd Edition. A copy is on reserve at the BU Science and Engineering library

Homework

  • Homework 1, Due Sep. 6th
  • Homework 2, Due Sep. 13th
  • Homework 3, Due Sep. 20th
  • Homework 4, Due Sep. 27th
  • Homework 5, Due Oct. 4th
  • Homework 6, Due Oct. 11th
  • No Homework due Oct. 18th
  • Midterm re-do is due Oct. 21st
  • Homework 7, Due Oct. 25th
  • Homework 8, Due Nov. 1st
  • Homework 9, Due Nov. 8th
  • Homework 10, Due Nov. 15th
  • Homework 11, Due Nov. 22th
  • Homework 12, Do the exploration in section 10.7 of the HSD-text, the following MATLAB codes ode_bz.m , bz.m , should help you. We will work interactively on this during the class period Nov. 25th. Due Dec. 2nd

    • Midterm and Final information

    There will be one in-class midterm during the semester. It will be held on Tuesday, October 15, during the class period. The problems will be roughly similar to examples done in class and those done in the homework.

    The final will be take-home, with problems being emailed out on Monday, December 16th. Problems will be similar to the those of the midterm, homeworks, and in-class examples. Logistics of the final will be discussed a few weeks prior. No collaboration, or use of the internet is allowed. You are allowed to consult your class notes, textbook, and any course handouts, as well as use any computer codes for plotting phase portraits you may have written up over the span of the semester.
  • Midterm Topics Guide

    • Grades

    Your course grade will be based on your homework scores (50%), your midterm (20%) and your final (30%). See the syllabus for guidance on how the homework problems will be graded. Records for assignment grades will be kept on the course blackboard website.

    Additional References, papers, and example codes mentioned in class

  • Codes to explore the Lorenz system ODE solver , vector field for ODE solver , solver which measures Lyapunov Exponents.
  • Codes to explore periodic and aperiodic dynamics in the forced Duffing oscillator ODE solver , vector field for ODE solver .
  • Codes to explore traveling waves in the Fisher-Kpp equation: PDE solutions , ODE solver , vector field for ODE solver . Here is the original paper
  • Codes to explore uncoupled harmonic oscillators and the reduced angular flow on a torus: dual_osc.m , torus.m
  • A MATLAB code which studies solutions and studies the Poincare map of the 1-D periodic harvesting problem in Chapter 1.
  • An example MATLAB code for Euler's method in 1-D.
  • "Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering," by Steven H. Strogatz, Second Edition. An online copy of the textbook can be found via the BU library here.
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