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ODEs, MA2051

Joseph D. Fehribach, B Term, 1995

Second Half Course Summary: Second Order ODEs & Systems

- Modeling: Newton's 2 Law
- A.
- Oscillations
- Spring Model (with forcing and damping):
- Pendulum Model:
(also linear version)
- Double Spring Model (not included on second test)

- B.
- Curve Ball Example

- 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)

- 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

- Major Theorems
- A.
- General Solutions for Linear, Second Order Equations
- B.
- Nonzero Wronskian Linear Independence

*Joseph D. Fehribach *

Tue Dec 12 17:57:54 EST 1995