Elementary Mathematical and Computational Tools For by CRC Press

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The ordered array is the set of positive integers 2. 1) 3. The initial conditions are F(1) = F(2) = 1 (note that the required number of initial conditions should be the same as the order of the equation). 1 Write a program for finding the first 20 Fibonacci numbers. Solution: The following program fulfills this task: N=18; F(1)=1; F(2)=1; for k=1:N F(k+2)=F(k)+F(k+1); end F It should be noted that the value of the different elements of the sequence depends on the values of the initial conditions, as illustrated in Pb.

What is the limit of each of the obtained sequences? b. How many iterations are required to obtain 2 accurate to four digits for each of the above initial conditions? c. Would any of the above properties be different for a different choice of A. Now, having established that the above sequence goes to a limit, let us prove that this limit is indeed A . 40) It should be noted that the above derivation is meaningful only when a limit exists and is in the domain of definition of the sequence (in this case, the real numbers).

An alternative method is, of course, to use arrays, in the manner specified in Chapter 1. 01:7; y=3*x-5; plot(x,y) To compare the two methods, we note that: 1. plot requires a user-supplied x-array (abscissa points) and a constructed y-array (ordinate points), while fplot only requires the name of the function file, defined previously and stored in a function M-file and the endpoints of the interval. 2. The fplot automatically creates a sampled domain that is used to plot the function, taking into account the type of function being plotted and using enough points to make the display appear continuous.

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