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).


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.