Solutions to problems in classical dynamics:

  • One should probably start with the Forced Simple Harmonic Oscillator, which is the way we can discuss resonance.
  • Discussion of the solution to the two body gravitational, also called Kepler Problem.
  • We all know that a particle under the influence of a constant gravitational field executes a parabolic trajectory.  The effect of drag makes the trajectory much more interesting and allows us to talk about Taylor series, as well as non-dimensionalization and scale analysis.

Some fun problems from dynamical systems:

Derivations from Linear and Nonlinear PDE


Problems in 2D Euler and Quasi-Geostrophy

Classical fluid instability

Some kinematic results from vector calculus