Math 3520
Differential Equations and Dynamical Systems

Professor Wickerhauser

NEWS

  • Octave commands orbitdia.txt to compute and plot orbit diagrams for the logistic function iteration.
  • Updated iterate.txt contains code to compute cobwebs for the cubic and logistic functions. The cobweb() function is also separated out in the file cobweb.txt
  • Updated HW 5 is now posted here and on Canvas.

EXAMPLE PROGRAMS

  • Example Octave commands orbitdia.txt to compute and plot orbit diagrams for the logistic function iteration.
  • Example Octave commands iterate.txt to compute and plot iterated dynamical systems.
  • Example Octave commands cobweb.txt to compute cobwebs showing convergence of iterations.
  • Example Octave commands lmax.txt to find local arg-maxes and max-values for a sampled function.
  • Example Octave commands lorenz.txt to plot a trajectory for the Lorenz equation.
  • Example Octave commands hw4-plot.txt for the computations and graphs needed to complete HW 4.
  • Example Octave commands contour.txt to plot the phase portrait (=flow field) for a gradient system together with the level curves (=contours) of its potential function, for Example 7.2.1, p.223 in the textbook.
  • Example Octave commands hw3-plot.txt to plot the graphs seen in the HW 3 model solutions.
  • Example Octave commands rk4a.txt to plot the flow field and some trajectories (by RK4) for the autonomous dynamical system in Example 6.1.1 of the text.
  • Example Octave commands lin2d.txt to plot example linear 2D flow fields.

Syllabus

Topics. Applications of ordinary differential equations: first-order equations, linear equations, and systems of equations. Long term behavior, bifurcation, chaos, strange attractor, and fractals.

Prerequisites. Math 233, Multivariable Calculus, and Math 309, Matrix Algebra.

Time. Classes meet Tuesdays and Thursdays, 10:00-11:20 AM in Cupples I Hall, room 207.
Lectures will be livestreamed via Zoom and videorecorded. Find the recordings under Zoom/CloudRecordings on the Canvas webpage for this class.

Text. The lectures will follow Nonlinear Dynamics and Chaos (Third edition) by Steven H. Strogatz, CRC Press, 2024. Author website.

Homework. You are encouraged to collaborate on homework and to work additional exercises from the indicated problem sections, although the homework grade will be based only on the assigned exercises.

Late homework will not be accepted. Problem sets will be assigned roughly biweekly as follows:
The lowest HW score will be dropped. The remaining HW percentages will be averaged with equal weights.

Tests. There will be one midterm examination in class on Thursday, March 5th, 2026, and one cumulative final examination on May 5th, 2026 in the classroom (Cupples I, room 207) from 6-8pm.
The midterm exam percentage will be replaced with the final exam percentage if this improves the course score. No makeup exams, or late or early exam dates, will be offered.

Grading. One score will be assigned for homework, one for the midterm examination, and one for the final examination. These three will contribute in respective shares of 40%, 30%, and 30% to the course score.

Letter grades computed from the course score will be as follows:

Course score at least: 90%80%70%60%
Letter grade at least: ABCD


Students taking the Cr/NCr or P/F options will need a grade of D or better to pass.

Office Hours. After class Tuesdays and Thursdays 12-1pm, or by appointment.

Questions? Return to M. Victor Wickerhauser's home page for contact information.