Fall 2009. Ma188.

Textbook: Fitzpatrick “Advanced Calculus” 2d edition.

Hw1 (due 9/10)

1. Prove the monotone convergence theorem for decreasing sequence.

2. Give the definition of lim x_n=−∞.

3^*. Find a sequence, for which every real number is a limit point. (Hint: instead of every real number, consider first every rational number and then apply Example 2.3 (p.24) and Theorem 2.20 (p.36)).

4. Read Fitzpatrick text sec. 1.3 (pp. 16−19), sec. 2.1 (pp. 23−35), sec. 2.3 (pp. 38−43), sec. 2.4 (pp. 43−47)

5. Solve # 2, 6, 15, 16 (sec. 2.1); # 2, 4, 8 (sec. 2.3)

Additional problems (recommended but not graded):

F. 1.1 # 3, 4, 5, 11, 12, 15, 16.

F. 1.2 # 1, 2, 3, 4, 5, 6, 7.

F. 1.3 # 1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 20, 22, 25a, 27.

F. 2.1 # 1, 3, 5, 7, 8, 9, 10, 11, 14, 17, 18.

F. 2.3 # 3, 5, 6, 7, 9, 11*(bonus).

Hw2 (due 9/17).

F. 2.2 # 2, 3, 4

Hw3 (due 9/24)

F. 9.1 # 1, 2, 3, 4, 5, 6, 7, 8.