eigA ans 23090 49965i 23090 49965i 19021 12842 vdeigA v Columns 1 through 3

# Eiga ans 23090 49965i 23090 49965i 19021 12842 vdeiga

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eig(A) ans = 2.3090 + 4.9965i 2.3090 - 4.9965i -1.9021 1.2842 [v,d]=eig(A) v = Columns 1 through 3 -0.1627 - 0.3412i -0.1627 + 0.3412i 0.4095 -0.3486 - 0.0541i -0.3486 + 0.0541i 0.7464 -0.7459 -0.7459 -0.1567 0.0000 - 0.4199i 0.0000 + 0.4199i -0.5006 Column 4 0.0735 0.9698 -0.1967 -0.1242 d = Columns 1 through 3 2.3090 + 4.9965i 0 0 0 2.3090 - 4.9965i 0 0 0 -1.9021 0 0 0 Column 4 0 0 0 1.2842 We note that all of the previous scripts were produced in MatLab and stored in a text file (test.txt). This is readily done by the MatLab commands: diary(’test.txt’) diary on MatLab entries here

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diary off The file test.txt will contain all the commands entered and the MatLab output in a text file, which can be easily read in any text editor. At this time we turn specifically to our murder problem. From the main lectures we saw that we needed to find the values for the heat coeﬃcient, k , and the time of death, t d , which solved the equations 22 + 8 e - k = 28 and 22 + 8 e - kt d = 37 . The first equation is equivalent to finding the zero of f ( k ) = 22 + 8 e - k - 28 . MatLab has an easy way to enter an inline function, and the software has the special function fzero , which can be used to numerically find zeroes of a function. This special function fzero has the form fzero(f, x0) , where f is the function of some variable, and x 0 is an initial guess where the zero might be. The sequence of commands below begins with obtaining more digits, the it creates the necessary functions and solves them. format long f = @(k) 22+8*exp(-k)-28; k = fzero(f,0.3) k = 0.287682072451781 ft = @(t) 22+8*exp(-k*t)-37; td = fzero(ft,-5) td = -2.185081100344673 These values agree well with the ones found in the lecture notes. As pointed out in lecture, many differential equations cannot be solved exactly. MatLab has powerful routines for numerically solving a differential equation. Here we use the example from our murder problem: dT ( t ) dt = - k ( T ( t ) - T e ) , T (0) = 30 , (1) where t = 0 corresponds to 8:30 AM, T e = 22 C is the room temperature, and k is the heat coeﬃcient found above using the body temperature at t = 1. Rather than working with line commands in the Command Window of MatLab, it is valuable to learn to create M-files for both functions and scripts. Before creating a new function or script file, it is a very good idea to point the Command Window to the directory where you are going to store your MatLab files. This is done in the window below greyed area for operations. We begin by creating a function, which is done by clicking on the New tab and selecting
• Fall '08
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