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,
exponents, structure of the general solution.
4/25: Linear systems with periodic coefficients: stability criterion,
instability curves. Example with piecewise-constant periodic coefficients.
4/27: Solution by variation of parameters: second-order linear non-homog.
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
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