Lecture Notes: Math 119A---Intro to ODE:

  • 1-Introduction
  • 2-Harmonic Oscillator
  • 3-Phase Portrait Scalar
  • 4-Existence and Uniqueness
  • 5-Picard's Method and the Contraction Mapping Theorem
  • 6-Energy and Over-damping
  • 7-Equations for Bead on Rotating Hoop---Overdamping
  • 11-Dimensions
  • 12-Non-dimensionalizing an equation
  • 13-Phase Plane
  • 14-More Phase Plane
  • 15-Linearized Rest Points
  • 16-Linearized Equations at Rest Points
  • 17-Nonlinear Stability at Rest Points
  • 18-Competetive Exclusion
  • 19-Conservative Systems
  • 20-Reversibility
  • 21-Lagrange's Equations
  • 22-Phase Portrait for Mass on Rotating Hoop
  • 23-Liauponov Stability Theorem
  • 24-Bead on rotating hoop with friction