- Exam 1
- Exponential Growth
- Qualitative Shape
- Existence and Uniqueness of Solutions
- Fixed Point Stability
- Sudden Population Collapse
- Homework 1
- Sketching Solutions
- Allee Effect
- Saddle-Node Collisions
- Collapse of a Population
- Homework 2
- Fixed Point Analysis
- Logistic Growth
- Predator Prey Model
- Homework 3
- Autonomy and Non-autonomy
- Lipschitz Condition
- Existence and Uniqueness (global, local)
- Bifurcation Diagrams
- Exam 2
- Phase Locking
- Periodic Solutions
- Conservative Systems
- Matrix Exponentials
- Ghost of the Saddle-Node
- Homework 4
- Euler's Method
- Laser Bifurcation
- Transcritical and Supercritical Bifurcations
- Homework 5
- Overdamped Limits
- Pitchfork Bifurcations
- Flow on a Circle
- Ghost of the Saddle Node
- Oscillator Entrainment
- Homework 6
- Hartman-Grobman Theorem
- Hartman-Grobman Homeomorphism
- Oscillator Entrainment
- Non-harmonic Oscillators
- Ghost of the Saddle Node
- Overdamped Limits
- Homework 7
- Matrix Exponentials
- Fast and Slow Directions
- Jordan Normal Forms
- Determinant-Trace Stability Analysis
- Circles under Invertible Maps
- Homework 8
- Damped Harmonic Oscillator
- Love Affair
- Index Theory
- The Brusselator
- Making a First-Order System
- Conservative Systems
- Homework 9
- Hopf Bifurcation Theorem
- Normal Form of Super/Sub-Critical Bifurcations
- Bifurcation Invariance up to Naming
- Homework 10
- One Dimensional Maps
- Iterative Periodic Orbits
- Similarity Dimension
- The Lorenz System's Dimension
- Box Dimension