- Lecture 1 August 29, 2024
Introduction, and Phase Plane technique:
and
.
- Lecture 2 September 6, 2024 Stability
Analyses, Theorem of existence and uniqueness, impossibility of oscillations
- Lecture 3 September 10, 2024
Higher order stability analyses, potential and
saddle node bifurcation
- Lecture 4 September 13, 2024 Normal
form of Saddle Node Bifurcation, transcritical bifurcation,
laser
- Lecture 5 September 17, 2024 Laser
Threshold, pitchfork bifurcation, supercritical and
subcritical
- Lecture 5 September 20, 2024
Subcritical bifurcation, hysteresis,overdamped bid on a hoop
- Lecture 6 September 24, 2024
?
- Lecture 7 September 27, 2024
Review of Chapter 2 and 3. Motion on a circle.
- Lecture October 1, 2024
Midterm
- Lecture October 4, 2024
Nonuniform oscillator, pendulum with a torque
- Lecture October 8, 2024
Torque, Fireflies and beginning of
- Lecture October 11, 2024
Solving the matrix system
with
matrix and verctor
- Lecture October 15, 2024
Solving
with complex eigenvalues/
- Lecture October 18, 2024
Deffective node and Classifications of the
systems
- Lecture October 22, 2024
Classification of
and
mathematics of love affairs
http://www.yurilvov.com/ODElecture15.pdf
- Lecture October 25, 2024
System of nonlinear equations
Examples. Lotka-Valtera system
- Lecture October 29, 2024
Midterm Review
- Lecture November 1, 2024
Midterm
- Lecture November 5, 2024
Lotka-Voltera and conservative systems
- Lecture November 8, 2024
Conservative and TIme Reversable systems
- Lecture November 12, 2024
Time Reversibility examples. Oscillator
- Lecture November 15, 2024
Oscillator and Limited Cycle. Van-der-Paul oscillator
- Lecture November 19, 2024
Lapunov, Dullac and Poincare-Bendixson
- Lecture November 20 (make up), 2024
Limited cycle, Lienard theorem and perturbation Theory
- Lecture November 22, 2024
Perturbation Theory Explained
- Lecture November 26, 2024
Perturbation Theory of the Van der Pol Oscillator
- Lecture December 3, 2024
?
- Lecture December 6, 2024 no lecture
- Lecture December 10, 2024
?