ws715 - Rob Bayer Math 55 Worksheet Homogeneous Linear...

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Unformatted text preview: Rob Bayer Math 55 Worksheet July 15, 2009 Homogeneous Linear Recurrence Relations with Constant Coefficients 1. Find the general solution to each of the following recurrence relations: (a) a n +2 = 2 a n +1 + 3 a n (b) a n = 6 a n- 1- 9 a n- 2 (c) a n = 4 a n- 1 (d) a n = 6 a n- 1- 8 a n- 2 2. Find the solution to the recurrence relation a n +2 = 5 a n +1- 6 a n ; a = 3 ,a 1 = 8 3. Find the solution to the recurrence relation a n = 6 a n- 1- 9 a n- 2 ; a =- 2 ,a 1 = 6 4. A theorem from analysis says that r is a double-root of r 2 + br + c if and only if r is also a root of the derivative, 2 r + b . Use this fact to show that if r is a double root of r 2 + br + c , then nr n is a solution to the recurrence relation a n +2 + ba n +1 + ca n = 0 Non-homogeneous Recurrence Relations 1. Determine whether each of the following are homogeneous or non-homogeneous. (a) a n = 3 a n- 1 + 2 a n- 2 + n 2 (b) a n = a n- 1- 4 a n- 2 + 1 (c) a n = a n- 1 + 7 a n- 2 + a n- 3 2. What is the “form” of your trial solution for each of the following. For convenience, the roots (and their2....
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This note was uploaded on 09/10/2009 for the course MATH 55 taught by Professor Strain during the Summer '08 term at Berkeley.

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