Math 6410 Homework assignments

Homework 1, Due Friday August 29:

Perko section 1.1: 1(d), 3, 4, 6.
Perko section 1.2: 2, 3, 5.
Prove that C[a,b] is a Banach space.
Prove that L(R^n) is a Banach space.
Perko section 1.3: 2, 3, 4, 8. Perko section 1.4: 6, 8.

Homework 2, Due Friday Sept 5:

Perko section 1.5: 5.
(oops--forgot to assign more problems!!)

Homework 3, Due Friday Sept 12:

Perko section 1.6: 3.
Perko section 1.7: 2(d).
Perko section 1.8: 8 (prove your answer), 9.
Perko section 1.9: 4(b).
Perko section 1.10: 3.

Homework 4, Due Friday Sept 19:

Perko section 2.1: 1, 3, 4.
Perko section 2.2: 4, 9, 11.
Check that Picard-Lindelof is stronger than Theorem 2.2.

Homework 5, Due Friday Sept 26:

Perko section 2.3: 1, 2(a), 4 (use the result from problem 2.3:3, which is implied by our result from class using contraction mapping theorem).

Homework 6, Due Monday October 6:

Perko section 2.4: 1(a), 2(b), 3.
Perko section 2.5: 6, 7.
Perko section 2.6: 1(a), 1(d), 3.

Homework 7, Due Friday October 10:

Perko section 2.7: 2, 3.

Homework 8, Due Friday October 17:

Perko section 2.8: 1.
Perko section 2.9: 3, 4, 7.

Homework 9, Due Friday October 24:

Perko section 3.1: 3, 9.

Homework 10, Due Friday October 31:

Perko section 3.2: 1, 5.

Final Homework. Due Friday December 5:

Perko section 3.5: 1.
Perko section 4.2: 1, 2.
Perko section 2.14: 1(a),(b).
Prove the Arzela-Ascoli Theorem.