MATH 840: Differential Equations 1

Fall 2006

Journal

Exercises meetings: Tuesday 1:30-2:20, BT 204.

HW9 - Sobolev Spaces.
Dimension 1
Imbeddings and compactness
Dim n>1

HW8 - Sobolev Spaces.
Gilbarg and Trudinger, Ch.7: Exercises 1 - 7 (for now...).

HW7 - Laplace's equation.
Gilbarg and Trudinger, Ch.2: Exercises 10, 11, 12.
Ch. 3: 1, 2, 10 (some might be tricky).

HW6 -- Lapace's Equation II

HW5 -- Lapace's Equation **UPDATE 10/16**
From Gilbarg & Trudinger, Ch.2, exercises *1 through 9, 13 and14*.

HW4 -- The method of characteristics (II):

HW3 -- The method of characteristics (Warm up):
From Evans' book, page 162-163:
Exercises # 2, 3, 4.

HW2 -- Dependence on parameters and data in ordinary differential equations:
From Chapter 2 of Sotomayor's book, page 43 and following:
Exercises #1, 2, 4, 5, 6, 9, 10.

HW1 -- Basics on ordinary differential equations:

From Chapter 1 of Sotomayor's book, page 21 and following:
Exercises # 11, 12, 13, 14, 15, 16, 17, *22 , 23, *24, 27, 31, @32.

I have used * to mark those that introduce standard numerical methods,
@looks like it might be tricky, but very interesting.
There is a large collection around Peano-Picard. There are some that introduce
comparison, others that look like they use Arzela-Ascoli. You should choose
a good sample rather than doing all those that focus on one single issue (and leaving
the rest). #11 and 12 are an absolute must!