Homework assignments

Homework 1, due February 4.

Exercises in Ch. 9 of Lang's book: 1, 2, 6, 7, 11.

Homework 2, due February 11.

Exercises in Ch. 9 of Lang's book: 4, 5, 9, 12, 15.

Homework 3, due February 18.

Exercises in Ch. 10 of Lang's book: 1, 2, 3, 4, 5.

Homework 4, due February 25.

Exercises in Ch. 12 of Lang's book: 1, 3, 6, 7, 9.

Homework 5, due March 10.

Exercises in Ch. 13 of Lang's book: 2, 6, 4, 5, 11.
Exercises in Ch. 14 of Lang's book: 1.

Test 1 on Friday, Feb. 29.

Homework 6, due March 24.

Exercises in Ch. 14 of Lang's book: 5, 6, 8, 10, 12.

Homework 7, due March 31.

Exercises in Ch. 14 of Lang's book: 13, 14.
Give examples to show that it is necessary to assume that both $E$ and $F$ are complete in the open mapping theorem.

Homework 8, due April 14.

Exercises in Ch. 16 of Lang's book: 1.
Exercises in Ch. 17 of Lang's book: 1, 3, 5.

Homework 9, due April 21.

Exercises in Ch. 17 of Lang's book: 6.
Exercises in Ch. 18 of Lang's book: 1, 6.

Homework 10, due May 5.

Exercises in Ch. 18 of Lang's book: 7, 9.
Prove the uniqueness of the weak derivative.
Let \Omega be the interval (-1, 1). Show that the function |x| is in W^{1, \infty}(\Omega), but not in H^{1, \infty}(\Omega).