08-02-07.mw

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I forgot to save the worksheet on this day, so I'm trying to recreate it from memory. Sorry about that.  Here goes:

First, we were talking about lists and sets and data and points and so on.  Sets are surrounded by {} braces and have no inherent order.  A list is surrounded by [] and has a fixed order.

 > {1,5,4};

 (1)

 > [1,5,4];

 (2)

Both lists and sets can have anything inside them, including another set or list:

 > { 1, [4,5], 2, {3}, apple};

 (3)

We can represent a point in the plane as a pair of numbers.  Here we have a list of points:

 > data := [ [1,2], [2,4], [4,8], [5,10]];

 (4)

 > plot(data);

 > plot(data,style=point);

 > plot(data,style=point,symbolsize=15,symbol=circle,color=blue);

 > plot(2*x,x=0..5);

We'd like to see both the line and the points on the same graph.  We can do this by assigning the plots to a variable, and then using the display command from the plots library to show them on the same plot.

 > linepic:=plot(2*x,x=0..5): pointpic:=plot(data,style=point,symbolsize=15,symbol=circle,color=blue):

 > pointpic;

 > plots[display]({linepic,pointpic});

Let's generate some data, and let maple find the appropriate line for us.  We'll use the seq command, so first let's play with the command itself.

 > seq(i^2,i=1..5);

 (5)

 > seq([i,i^2],i=1..5);

 (6)

Now let's make some points on the line y=x/2

 > pts:=[seq([x,x/2],x=0..10)];

 (7)

 > with(CurveFitting);

 (8)

 > PolynomialInterpolation(pts,x);

 (9)

 > pts2:=[seq([x,x/2],x=0..5),[5.5,6.5],seq([x,x/2],x=6..10)];

 (10)

 > PolynomialInterpolation(pts2,x);

 (11)

 > with(plots):

 > display(  [plot(pts2,style=point,symbolsize=15,symbol=circle,color=blue),   plot(PolynomialInterpolation(pts2,x),x=0..10)]);

 > display(  [plot(pts2,style=point,symbolsize=15,symbol=circle,color=blue),   plot(PolynomialInterpolation(pts2,x),x=-1..11,y=-10..20)]);

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