Plotting and Graphical Analysis using Maple Thomas LoFaro Gustavus Adolphus College

One of the great things about Maple and similar software is its ability to make great plots. In this section I'll just provide you with some of the basics. To plot a single function we simply use the plot command the basic syntax is plot(expr, x=xmin..xmax). LUklcGxvdEc2IjYkLCYqJEkieEdGJCIiIyIiIiEiIkYqL0YoOyEiJCIiJA==

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We can easily plot multiple functions on the same graph by enclosing the expressions in curly brackets ({}) as in the following example. LUklcGxvdEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkPCRJInhHRicsJiokRioiIiMiIiIhIiJGLi9GKjshIiQiIiQ=

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Plots can be modified (a little bit) or exported to a file by right-clicking on the graph. A pull down menu will appear and you can then choose from a variety of options. Plots can also be resized (useful if you are writing a report) by left-clicking on the graph. A frame will appear around the graph and you can adjust the size using the small boxes along the edges. When you click on a graph and it is framed then a coordinate box appears in the upper left of the Maple window (where the Text and Math buttons usually are). This can be useful when you need to estimate intersections and other features of the graph. Another useful tool is the Plot Builder Assistant. Find this under the Tools->Assistants->Plot Builder menu. It is a slow way to make a simple graph but if you want to add a bunch of options to make it look nice then it is easier to use the Plot Builder Assistant than looking up all of the options in the manual. Try using the Plot Builder Assistant to make a graph of your own. 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

Maple does not have a built in facility for doing graphical analysis. However, I have written a program that will do it for you. Before we start, we need to load a couple of special graphing packages QyYtSSV3aXRoRzYiNiNJJnBsb3RzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlISIiLUYkNiNJKnBsb3R0b29sc0dGKEYr JSFH Now comes the programs. The first simply generates the lines for graphical analysis. The second one is the important one. I've included comments (in blue) for those of you who want to try and figure out how this works. QyQ+SSlnZW5saW5lc0c2ImYqNiRJImxHRiVJImlHRiU2JEkieEdGJUkieUdGJUYlRiVDJT44JC1JI29wRyUqcHJvdGVjdGVkRzYkOSU5JD44JS1GMTYkLCZGNCIiIkY7RjtGNTckLUklbGluZUdGJTYkNyRGL0YvNyRGL0Y3LUY+NiRGQTckRjdGN0YlRiVGJSEiIg== 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 The name of the function to do graphical analysis is cobweb (sometimes these figures are called cobweb plots) and its synax is cobweb(expr, range, xinit, ntrans, ntot) where expr is the expression to be iterated, range is of the form x=xmin..xmax and the the plotting domain, xinit is the initial condition, ntrans is the number of transient iterations (the number you don't want plotted), and ntot is the total number of iterations. Let's say we want to do graphical analysis of f(x) = 3.4*x*(1-x) with an initial condition of .5 showing the first 10 iterates. LUknY29id2ViRzYiNicsJComSSJ4R0YkIiIiLCZGKUYpRighIiJGKSQiI01GKy9GKDsiIiFGKSQiIiZGK0YwIiM1

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If we only want to see the last 4 iterates then this is what we do LUknY29id2ViRzYiNicsJComSSJ4R0YkIiIiLCZGKUYpRighIiJGKSQiI01GKy9GKDsiIiFGKSQiIiZGKyIiJyIjNQ==

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Do problems 1,2,4 at the end of chapter 4 in Devaney. From each problem do part (c) by hand (you can use Maple to plot the function) and using Maple.

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