By Raymond Pearl
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Extra info for A Further Note on the Mathematical Theory of Population Growth
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.
Axis supports the arguments equal and square, which makes the current graphs aspect ratio 1. Plots contour lines of a surface. Clears all variables from the workspace. Clears ﬁgure. Runs a sequence of commands a given number of times. Returns the pixel image of a movie frame. Online help. Holds the plot axis with existing graphics on, so that multiple ﬁgures can be plotted on the same graph (release the hold of the axes). if length load linspace meshgrid mesh meshc min max mean moviein movie orient plot plot3 polar pol2cart print quit or exit rand randn subplot save std stem view who xlabel, ylabel, zlabel, title (x>=x1) © 2001 by CRC Press LLC Conditional evaluation.
9 If the parametric equations of a curve are given by: C: x = cos(t), y = sin(2t), and 0 < t < 2π where the initial point is at x = 1, y = 0, and the ﬁnal point is at x = 1, y = 0. The curve so obtained is called a Lissajous ﬁgure. It has the shape of a ﬁgure 8 with two nodes in the x-direction and only one node in the y-direction. What do you think the parametric equations should be if we wanted m nodes on the x-axis and n nodes on the y-axis? Test your hypothesis by plotting the results. 3 Plotting a 3-D Curve Our next area of exploration is plotting 3-D curves.
A Further Note on the Mathematical Theory of Population Growth by Raymond Pearl