| Lecture 1 | Introduction | Lec1.pdf,
Lec1_annotated.pdf Lorenz equations (butterfly) movie: LorenzButterflyMovie KB_1a.pdf |
| Lecture 2 | 1D Flows, Fixed Points, and Stability | Lec2.pdf,
Lec2_annotated.pdf, KB_2a.pdf, WheelC_Movie, WheelV_Movie |
| Lecture 3 | Existence and Uniqueness (1D diff eq's) | Lec3.pdf, Lec3_annotated.pdf |
| Lecture 4 | Potential Fields, Numerical Methods | Lec4.pdf, Lec4_annotatedA.pdf |
| Lecture 5 | Bifurcations in 1D: Saddle Node, Transcritical | Lec5.pdf, Lec5_annotated.pdf |
| Lecture 6 | Bifurcations in 1D: Pitchfork (Supercritical and Subcritical) | Lec6.pdf, Lec6_annotated.pdf |
| Lecture 7 | Linear Systems in 2D: Overview, Definitions, Examples | Lec7.pdf, Lec7_annotated.pdf |
| Lecture 8 | Phase Portraits in 2D: Linear; Nonlinear; Linearized | Lec8.pdf,
Lec8_annotated.pdf Lec8_damped_springmass.m, run_bead_on_hoop.m, bead_on_hoop.m, Alinearized_example.m, |
| Lecture 9 | MIDTERM REVIEW | Lec 9: Midterm Review Notes |
| N/A | Midterm Exam | Midterm Exam |
| Lecture 10 | Conservative Systems; Reversible Systems | Lec10.pdf, Lec10_annotated.pdf |
| Lecture 11 | Nonlinear Centers; Homoclinic Orbits; Heteroclinic Paths | Lec 11.pdf,
Lec11_annotated.pdf, Please also see: Pendulum_Comments.pdf |
| Lecture 12 | Limit Cycles: Index Theory, Lyapunov Fns | Lec12.pdf,
Lec12_annotated.pdf rabbits_and_sheep.mp4, rabbits_and_sheep.mov |
| Lecture 13 | Limit Cycles: Poincare-Bendixson Thm, Lienhard Thm | Lec 13.pdf,
Lec13_annotated.pdf, Please also see: Recitation 5 Notes |
| Lecture 14 | (Lienhard Thm, Cont.) / Bifurcations in 2D | Lec14.pdf, Lec14_annotated.pdf |
| Lecture 15 | Bifurcations in 2D / Lorenz System (Chaos) | Lec 15.pdf, Lec15_annotated.pdf |
| Lecture 16 | Chaos and Strange Attractors (Part II) | Lec16.pdf, Lec16_annotated.pdf |
| Lecture 17 | 1D Maps, Revisited: Lorenz map, logistic map | Lec 17.pdf, Lec17_annotated.pdf |
| Lecture 18 | Fractals and Their Dimensionality | Lec18.pdf, Lec18_annotated.pdf |
| Lecture 19 | Strange Attractors; Course Review | Lec 19.pdf, Lec19_annotated.pdf |
| Final Exam | Topics and Problems | Final Exam Topics,
Final Exam Hints Note: There will likely be (about) 6 problems, with a goal of spanning the 5 areas listed in "Final Exam Topics". Since Calculators and computers are prohibited, questions will focus on basic understanding, "doable" analytic calculations, and graphical interpretations. |