MATH 840 / 841: Differential Equations 1 & 2
Syllabus - Fall 2006 & Spring 2007
Instructor: Marianne Korten
Office: Cardwell 234, 532-0567
Exercises meetings and office hours:
TBA.
Course description, and books we will use:
Just a few words to add to the description you find in the catalogue:
For quasilinear first order equations I will likely use Evans' book and some notes of a course
James Serrin taught long ago at the University of Minnesota. For this I will need a bit of ODEs,
which I will take from Sotomayor's book.
I will teach Laplacian /elliptic equations from chapters 1 & 2 from Gilbarg and Trudinger's
book.
At this point one naturally needs a bit of Sobolev Spaces, and distributions, then one can do
some toy problems in variational calculus (I will use Elsgolts' little book for calculus of
variations, and some old class notes of Calderon's for distribution theory).
For Burger's equation and shock waves I will use chapters 15 and 16 from Smoller's book.
For heat and wave equation I will likely use Evans' book.
For separation of variables & co I will use Weinberger's book.
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I like how these books work the material, and their authors are masters of their trade, which is always good.
I will give you exercises, and schedule a weekly meeting time to watch you / help you do them.
The idea of the course is to give you a sample of what people do in PDEs and how they go
about it, seen with the taste of someone who makes her living with PDEs. It should also give
you a safe starting point and a pretty complete sample for when you need to teach PDEs in your
future jobs.
Except for Sotomayor's, the books I metioned are in the library (I haven't checked on
Weiberger's, but Dover has it for cheap).
Grading policy:
Attendance and participation are requiered. You are expected to
complete the homework you will be assigned regularly,
and not fall behind, although it will not be collected nor graded.
There will be one midterm and one final. Final grades will be
based on witten work and as follows: 50% for the midterm,
50% for
the final. Some homework exercises will reappear in the midterm and the
final (!).
Here I will post your (roughly weekly) assignments.