Math 293 Course news:
1) Prelim 2 on Thursday 10/31/96 includes HW9 due 10/30/96.
Anything from the lecture, HW (turned in or otherwise),
or coverred parsts of the text, could be on the test.
Solutions to HW9 will be passed out on Wed 10/31/96.
This prelim will have a similar format to the last prelim.
Three problems. Maybe one hard bonus.
One of the three problems may be somewhat harder so as
to distinguish the better students more by their
knowledge than their mistakes.
Please go to the scheduled rooms (to be
announced), line up in columns,
Put all books and bags at the front of the room or
in the isles (no books, coats, notes, paper,
calculators, or bags on or under seats).
2) Syllabus change.
As the recent lectures and HW8 make evident, the syllabus
has changed slightly in recent weeks. In particular:
*sections 5.1 and 5.2 went an extra 3 lectures.
*section 5.3 will not be coverred,
*sections 6.1 - 6.5, rather than taking 3 lectures, are
being condensed into one lecture on monday 10/21/96 and
are obviously not being coverred too deeply.
We are, at least at this time, planning to get back on
the schedule handed out at the start of the semester
starting with the lecture on Wednesday 10/23/96 where
we start in with multi-variable calculus in Thomas and
Finney.
3) Guide to reading in Chapter 6 of E&P:
READ: section 6.1 on Stability and Phase plane, pgs 333-341.
Don't be too particular about the technical definitions
of stability but make sure you get the idea.
Words to know: 'phase plane',
'trajectory',
'direction field',
'critical point=fixed point=equilibrium solution',
'stable vs unstable'.
Don't worry about the categorization of nodes into proper,
improper, saddle, spiral, etc.
SKIP or SCAN: section 6.2 on linear and almost linear systems.
SCAN: section 6.3 on predator prey models to get a sense of the
role of the phase plane in studying such applications.
SCAN: section 6.4 on non-linear mechanics to see roughly how mechanics
can lead to non-linear ODEs.
READ: section 6.5 on Chaos, skipping stuff that depends on knowing
Mathematica. The key is to get a sense of what kind of
equations can lead to wild behaviour.
-Andy Ruina, ruina@cornell.edu, office hrs thursdays 1-5 (TH 102, near stairs)
Math 293 on the net: http://tam.cornell.edu/faculty/ruina/www_293/home.html