week12 - Math 43 Fall 2007 B Dodson Week 12 Finish...

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B. Dodson Week 12: Finish suggested homework 10, . . . Graded Homework 12: Section 3.7 - 2, 4; and 4.6 - 7, 11, pg. 356; due Wed. Dec. 5 From 4.6 we will ONLY cover pp. 322-326 (Markov chains) and pp. 327-329 (population growth). ————— Finally, we’ve gone over the text’s Example 3.46 from Section 3.7, pp. 228-231 and discussed Examples 3.65 and 3.66. In each case we have an initial state vector ±x 0 and then subsequent states ±x 1 , ±x 2 , . . . , ±x k , . . . The states are related by a transition probability matrix P (or by a Leslie matrix L ) with ±x i = P±x i - 1 , so ±x i = P i ±x 0 (or the same equations with P replaced by L ). In each case we get a steady state given by an eigenvector of the matrix. For the cases that occur in the applications the matrix P can be diagonalized; resp. we only need the positive eigenvalue, and we determine the steady state (resp. rate). Finally, we recall (below) that we have observed that the material of 4.4
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week12 - Math 43 Fall 2007 B Dodson Week 12 Finish...

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