Principles of Analysis

Homework Assignment #9

Due Wednesday, November 20, START of Class

Homework should be turned in at the BEGINNING OF CLASS. All problem numbers refer to Bilodeau and Thie's book, the required text for the course. You should write up solutions neatly to all problems, paying particular attention to your arguments and proofs. A nonempty subset will be graded. You are strongly encouraged to work on these problems with other classmates, although the solutions you turn in should be your own work.

Section 4.3
Problems:   11a, 11c, 11e, 12a, 12c, 18, 19a

Hint: Problems 18 and 19a are nice applications of the Mean Value Theorem. Try using proof by contradiction for number 18. Suppose that p is also a fixed point. Apply the Mean Value Theorem on the interval [p,q].

Note: Problem #18 suggests a nice extra credit problem, proved in most dynamical systems courses. See problem #5 in the Extra Credit problems for details.

Section 5.1
Problems:   1, 3a, 10, 11

Section 5.2
Problems:   1a, 1b, 4, 5a, 5b, 12

Hint: In problem #5, try finding an upper bound for the integrand over the interval of integration.