syllabus & additional info (spring 2011, 1st half)
(tentative:
do check back every week for changes)
the problem sets to be solved
each week in the corresponding
practice sessions (werkcolleges;
last hour of the class)
can be found in the lecture notes.
these problem sets are to be handed in
as homework every two weeks.
homework is mandatory,
in the sense that
it helps determine
your final grade.
homework will be disseminated every week
in class & through this page.
nevertheless,
homework is to be turned in
only once every two weeks.
collaborations are encouraged;
it goes without saying that
it is strongly recommended
that you put as much effort
in each homework set
as is needed to master the material.
every team is only required to turn in
only one howework set.
lecture notes
available in pdf format
(updated weekly; last update 2011.05.23)
— part i : a. zagaris —
lecture #01 (2011.02.08)
(some introductory remarks on the subject)
a regularly perturbed asymptotic problem
a singularly perturbed asymptotic problem
suggested reading: Holmes, §1.1-2 & 1.5
lecture #02 (2011.02.15)
order symbols
asymptotic expansions
a singularly perturbed transcendental problem
(self-study: use the lecture notes
and problem 02 of this week's HW)
suggested reading: Holmes, §1.3-4 & 1.7
lecture #03 (2011.02.22)
regularly perturbed ODEs
singularly perturbed ODEs
boundary layers and matching
suggested reading: Holmes, §1.3-4 & 1.7
lecture #04 (2011.03.01)
Fenichel theory
suggested reading: these notes (based on C.K.R.T. Jones's article) & T. Kaper's introductory AMS article
lecture #05 (2011.03.08)
(applications of Fenichel theory)
relaxation oscillations in a predator-prey model
relaxation oscillations for Rayleigh's equation
suggested reading: this week's notes, as well as Holmes, §6.5 and O'Malley, §2.G
lecture #06 (2011.03.15)
the Poincaré-Lindstedt method
the method of multiple scales
suggested reading: Holmes, §3.1-3
and Kevorkian-Cole, §4.1-2
lecture #07 (2011.03.22)
metastable patterns in a reaction-diffusion system
suggested reading: the Fusco-Hale j. dyn. diff. eqs. article and as much of the Carr-Pego comm. pure appl. math
article as you can take
— part ii : a. muntean —
lecture #08 (2011.03.29)
formal asymptotic homogenization pt.I
suggested reading: see notes
lecture #09 (2011.04.05)
formal asymptotic homogenization pt.II
suggested reading: see notes
lecture #10 (2011.04.12)
applied functional analysis
suggested reading: see notes
lecture #11 (2011.04.19)
rigorous homogenization for linear elliptic PDEs
suggested reading: see notes
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