Homework is due at the beginning of class on Fridays.

Due April 4: From the text: T1.1, 1.2; C1.1 (try at least four different initial values).
Additional exercises:
E1) Find the fixed points of the map f(x) = x^2 (i.e, x squared). Plot or sketch the cobweb plots for {x_0, ..., x_5} for the initial conditions x_0 = 1/2, -1/2.
E2) Find the fixed points of the map f(x) = cos(pi x). Plot or sketch the cobweb plots for {x_0, ..., x_7} for the initial conditions x_0 = 1/2, -3/4, -4/5.

Due April 11: From the text: T1.3, 1.5; C1.2, 1.3; exercises 1.1, 2, 5, 10 from the end of the chapter.

Due April 18: T1.12, 1.13, 1.14a, 1.16; C1.4, 2.1; exercises 1.11, 1.12, 1.17 from the end of the chapter.

Due April 25: T2.2-6; exercises 2.1, 2.2 from the end of the chapter. Problems T1.12 and E1.17 from last week can be resubmitted if you'd like.

Due date changed! Due Monday, May 5: T2.7-10; C2.2; exercises 2.3, 2.4, 2.7, 2.8 from the end of the chapter. (You can use Mathematica to help with the linear algebra and equation solving!)

Due May 9: Exercises 2.5, 2.6 from end of Chapter 2; C3.1 (don't try to actually compute the limit -- choose a reasonable tolerance and keep increasing n until the change in value stays within your chosen tolerance).

Due Monday, May 16: T3.1, 3, 4, 7; exercises 3.1, 15 from end of Chapter 3.
Hints: To do EoC3.1.e, try showing that the map for a = 2 is conjugate to the logistic map with a = 4 (the map the book's now calling G); look for a conjugacy map of the form C(x) = b + c x for some constants b and c. If you can establish conjugacy, you can use everything you know about G.
I recommend using the computer to do EoC3.15, but you can do it by hand if you prefer.

Due Wednesday, May 28: Exercises 3.4, 11a,b, 13 from end of Chapter 3; C4.1.
Hints: Use hints at the back of the book!

Due Friday, June 6: Exercises T4.7, 4.1 and 4.2a, b from end of Chapter 4; T7.1, 7.3, 7.5, 7.8, 7.9, and 7.5 from the end of Chapter 7; T9.1, 9.2, and 9.1, 9.2 from the end of Chapter 9.
Hints: Use hints at the back of the book!

Specifications and recommendations

Computer work can be submitted by emailing me a PDF file (slightly preferred) or submitting a hardcopy with the rest of your assigment. Please label each problem clearly. If you refer to key features of a plot or table in your write-up, clearly identify that feature in your submission (e.g. label a particular point either directly in the plot or by circling it or putting an arrow to it on a print out).

Late homework will be discounted and, at the discretion of the grader and/or the instructor, may not be accepted.

Your homework should be neatly written and well-organized, with the pages securely fastened together and your name on every page. Many of the exercises involve several nontrivial steps; make it clear to your readers (and yourself!) what it is you're doing at each step.

Clearly number the exercises and try to submit them in numerical order; if any problems are out of sequence, indicate that at the beginning of the assignment. (You don't need to solve them in order, just submit them in order.) The grader should not have to hunt through several pages to find a particular problem.

Computer difficulties do not justify late or incomplete assignments.
 

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