<p>Turn on mic!</p><p>“When is the exam?” ..?.. “Next Tuesday!”</p><p>Read exam cover sheet</p><p>Questions on anything?</p><p>Discuss practice test: http://jamespropp.org/322/practice-second.pdf http://jamespropp.org/322/practice-second-sols.pdf</p><p>Return homeworks old and new; show unclaimed stuff</p><p>Group work: S(n) + S(n–1) = (–1)n, S(0) = 1. The characteristic equation is x + 1 = 0, which has –1 as a root, and the right hand side is an exponential function with –1 as the base, so there must be a formula for S(n) of the form S(n) = (An+B)(–1)n. Solving for A and B, we get S(n) = (n+1)(–1)n.</p><p>Group work: S(n) = S(n–2), S(0) = 2, S(1) = 0. Group work: S(n) = – S(n–2), S(0) = 2, S(1) = 0. (Make sure someone in your group knows about complex numbers!) This last example leads to the Discrete Fourier Transform!</p><p>There’s a strong parallel between recurrence relations and differential equations. Compare: Question: What are the solutions to the recurrence relation S(n) – S(n–1) = 1? Answer: S(n) = n+C. Question: What are the solutions to the differential equation f ′(x) = 1? Answer: f(x) = x+C.</p><p>Use social media (e.g., Rate My Professor) to report on your experience in this class.</p><p>What do you think of the money-for-mistakes gimmick? What do you think of the easter egg gimmick? What do you think of holding the exam on the last day of class?</p><p>Good luck Tuesday!</p>