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; SOC B59
Office Hours :Tu 2:30p-3:30p (in person), W 11a - 12:10p (in person), Thu 11-12p(zoom) or by appointment (please provide your availability when requesting an appointment). 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 . An electronic copy can be found through the BU library website here .

Homework

  • Homework 1, Due Sep. 9th
  • Homework 2, Due Sep. 16th
  • Homework 3, Due Sep. 23rd
  • Homework 4, Due Sep. 30th
  • Homework 5, Due Oct. 7th
  • Homework 6, Due Oct. 14th
  • Homework 7, Due Oct. 28th
  • Homework 8, Due Nov. 4th
  • Homework 9, Due Nov. 11th
  • Homework 10, Due Nov. 18th
  • Homework 11, Due Dec. 9th

    • Midterm and Final Project Information

    There will be one take-home midterm during the semester. They will be given out onOctober 14th and November 18th during the class period. The problems will be roughly similar to examples done in class and those done in the homework.

    There will also be a final project. You will be expected to read about, research, or investigate a topic related to the course, write an expository paper, and present on it during the last few days of class. More details and due dates/milestones for this are listed in the course syllabus.

    Grades

    Your course grade will be based on your homework scores (45%), your midterms (15%) each and your final project (25%). 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 the BZ system ODE solver , vector field for ODE solver .
  • Codes to explore uncoupled harmonic oscillators and the reduced angular flow on a torus: dual_osc.m , torus.m
  • A set of matlab codes to solve 2-D and 3-D systems of equations in matlab. The files vf.m defines a matlab function file which calculates the vectorfield, and is used iin ODE_VectorField.m, a script which plots the vector field (one has to alter the lines 7 and 8 to be for the desired vector-field) and plots trajectories for range of initial conditions. One can edit the range of initial conditions on line 6 in the definition of x and y. For example just set x = x0 and y = y0, for two numbers x0 and y0 to plot just one trajectory.
  • A reference on tipping points in climate and ecological systems
  • 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.
  • Last Modified
    The views and opinions expressed in this page are strictly those of the page author. The contents of this page have not been reviewed or approved by Boston University.