Nonliear Dynamics and Chaos I (MATH 721)

Syllabus: Click here to download (PDF).
Lectures: 1:00pm-2:15pm, M/W, in AB 634
Instructor Office Hours: Tuesday 11am-noon, Thurs 3pm-4pm, or by appointment, in 220 DMSC.

WebCampus/Canvas will be used for this course: https://wcl.unr.edu

Note: This webpage is only an archive of this course. Current students: please use webcampus/canvas.

Tentative Schedule

Week Mon Weds Notes
1: 8/26-8/30 Syllabus (PDF) & Introduction Background & 1D Dynamics (Ch. 1, 2)
2: 9/2-9/6 Labor Day (No Class) 1D Dynamics (Ch. 2,3)
3: 9/9-9/13 1D Dynamics (Ch. 3) Flows on the circle (Ch. 4) Hw 1 (due next week)
4: 9/16-9/20 Flows on the circle (Ch. 4) 2D Dynamics (Ch. 5,6) Hw 2 (due next week)
5: 9/23-9/27 Phase Plane (Ch. 6) Numerical Solutions to ODEs
6: 9/30-10/4 Phase Plane (Ch. 6) Exam 1 Review
7: 10/7-10/11 Exam 1 Eq. stability in n-dimensions;
Projects
See book chapter (shared via Canvas)
8: 10/14-10/18 Phase Plane (Ch. 6, up through 6.4) Conservative & Reversible Systems; Index Theory (Ch. 6)
9: 10/21-10/25 Finish Ch. 6; Limit Cycles (Ch. 7) Limit Cycles (Ch. 7) Project files:
project-LaTeX-files.zip
(proposal due 15 Nov)
Hw 3 (due next week)
10: 10/28-11/1 Limit Cycles (Ch. 7) Guest Lecture (Dr. Grudzien): Intro to Chaos, Lyapunov Exponents
11: 11/4-11/8 Lienard systems; Fast-slow systems Averaging Method
12: 11/11-11/15 Veterans Day (No Class) Bifurcations revisited (Ch. 8) Project Proposals Due!
13: 11/18-11/22 Bifurcations revisited (Ch. 8) Center Manifolds & Normal Forms EXAM 2
14: 11/25-11/29 Chaos & discrete maps (Ch. 9,10) Chaos & discrete maps (Ch. 9,10)
R code for logistic map: logistic_map_bifns.R
Thanksgiving Week
15: 12/2-12/6 Computational bifurcation analysis Advanced Topic: TBD
16: 12/9-12/13 Project Presentations Prep Day (No Class)
17: 12/16-12/20 Final schedule for 9:50am-11:50am --