4/20: Non-homogeneous linear systems (section 7.7); solution by "undetermined

coefficients" , variations of parameters formula. Resonance.
Example involving

Fourier series. HW8 (due 4/27): 1(b)(c), 4,6,10.

4/23: Linear systems with periodic coefficients: period advance map,
characteristic

exponents, structure of the general solution.

4/25: Linear systems with periodic coefficients: stability criterion,
parametric resonance,

instability curves. Example with piecewise-constant periodic
coefficients.

4/27: Solution by variation of parameters: second-order linear non-homog.
eqns. Non-linear

non-autonomous 2nd order eqns: Example (forced Duffing, formal
perturbation expansion),

general existence theorem/stability criterion.

4/30: Stability for forced non-linear oscillations (examples). Parametric
resonance (examples).

FINAL EXAM

The exam will consist of six problems, as follows:

PART ONE: one problem from Exam 1

PART TWO: one problem from Exam 2

PART THREE: two problems, which may or may not
be taken from Exam 3- see

the list of topics covered in this web site,
under "part three".

PART FOUR: two problems: see list of topics
above.