This announces Math 531-532 (Ordinary Differential Equations)
that I am scheduled to teach in Fall'16-Spring'17.
As we are running this sequence every 3-4 years only, for most of
you, this means that you should register for it *now* if you are
interested to take it *at all*.


Prerequisites:
While Math 431 can be used as a `warm-up' for 531-532, it is *not* a
prerequisite. The mathematical prerequisites are the sophomore level
DiffEq course, and some core analysis skills like are contained in
the 447-448 sequence. Students with a good abstract proof background
in any area should be able to blend in, even if they have not completed
447-448. The specifically required contraction mapping principle (aka
Banach fixed point theorem) will be explained in class to keep the
course sufficiently self-contained.

Purposes:
The course serves several audiences: <HONMATH may skip to (*6*)>

(*1*) those interested in Diff-Eq in general.
The ODE sequence is independent of the PDE sequence 535-536, the methods
and questions are somewhat different between the 2 sequences.

(*2*) pure math folks in areas like differential topology or
differential geometry, in which the flow of vector fields plays a role.
While I will hardly address the manifold case that is most interesting
for this audience, the generalization of results to this case will be
rather automatic for *this* audience.

(*3*) Applied folks (e.g., in Math Biology), who clearly benefit from
both the ODE and the PDE sequence. I will include some core material from
*qualitative* ODEs (dynamical systems) that is very relevant for this
audience: namely stability, Lyapunov functions, asymptotic stability,
limit sets, Poincare-Bendixson, and hopefully a bit more.
(For the `hopefully a bit more' part, I may skip some proofs.)

(*4*) Folks interested in physics applications will find some
Sturm-Liouville theory as well as power series methods (regular
singular points) included.
(The latter may or may not have been covered in 431, depending on instructor.)
Therefore classical special functions like Bessel, Airy, hypergeometric
will be covered and demystified.

(*5*) While the course is mainly proof based, the rather self--contained
nature of the material makes the course practical for MS candidates looking
for a master thesis or an exam based option.

(*6*) The course is perfectly feasible for Honors undergraduates; it
could be taken in lieu of a senior honors sequence, or (subject to
the applicable policy fine print) for graduate credit while enrolled
as a senior undergraduate. I would generally assume our Hons concentration
cohort to be prepared for the course if they have taken a 400 level proof
oriented sequence already, or are at least concurrently taking 447-448
(or even just 447-443). It could give rise to work towards an Honors
thesis, if desired.


Textbook: Gerald Teschl; Ordinary Differential Equations and
Dynamical Systems. AMS GSM#140 ($64 sticker price;
$41 on amazon right now)

Please contact me for any questions you may have.

Jochen Denzler