ODEs, MA2051

Joseph D. Fehribach, B Term, 1995

Second Half Course Summary: Second Order ODEs & Systems

1. Modeling: Newton's 2 Law

   A.

   Oscillations

   1. Spring Model (with forcing and damping):
   2. Pendulum Model: (also linear version)
   3. Double Spring Model (not included on second test)

   B.

   Curve Ball Example

2. Solution Methods

   A.

   Method of Characteristics (for equations and systems)

   B.

   Undetermined Coefficients (for equations)

   C.

   Numerical Solutions: Euler's Method (for equations and systems)

   D.

   Variation of Parameters (for systems)

3. Classification, Terminology

   A.

   physical law, ``proportional to''

   B.

   linear, homogeneous, principle of superposition

   C.

   homogeneous solution, particular solution, general solution

   D.

   direction fields, graphics

   E.

   linear independence, Wronskian

   F.

   Euler's Formula:

   G.

   phase angle, underdamped, overdamped, critically damped, resonance

   H.

   steady state (equilibria), perturbation, linearly stable/unstable

   I.

   phase plane

4. Major Theorems

   A.

   General Solutions for Linear, Second Order Equations

   B.

   Nonzero Wronskian Linear Independence